Measures of Central Tendency and Dispersion

473 Practice MCQs available for CA Foundation

Paper

Paper 3: Quantitative Aptitude

Exam Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

Key Terms

Current Ratio

A liquidity ratio that measures a company's ability to pay its short-term liabilities using its short-term assets. Formula: Current Assets ÷ Current Liabilities. The ideal ratio is 2:1.

Quick Ratio

A stringent liquidity ratio (also called Acid-Test Ratio) that measures the ability to meet short-term obligations using only the most liquid assets, excluding inventories and prepaid expenses. Formula: (Current Assets − Stock − Prepaid Expenses) ÷ Current Liabilities. Ideal is 1:1.

Income Elasticity of Demand

Measures the responsiveness of quantity demanded to a change in consumer income. Formula: YED = % Change in Quantity Demanded / % Change in Income. Positive YED indicates a normal good; negative YED indicates an inferior good.

Cross Elasticity of Demand

Measures the responsiveness of the quantity demanded of one good (X) to a change in the price of another good (Y). Formula: XED = % Change in QD of X / % Change in Price of Y. Positive XED → substitutes; Negative XED → complements.

Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

All 473 Questions

3086
If the range of 28,22,40,20,15,50\displaystyle 28, 22, 40, 20, 15, 50 is
MCQ
3115
If the S.D. of the 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 30\displaystyle \sqrt{30} then the value of n\displaystyle n is
MCQ
3116
If the variance of 5,7,9\displaystyle 5, 7, 9 and 11\displaystyle 11 is 4\displaystyle 4, then the coefficient of variation is:
MCQ
4069
A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is
MCQ
4070
If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are
MCQ
4071
Which of the following is not a method of dispersion?
MCQ
4072
Find out co-efficient of variation, if N=14\displaystyle N = 14, Σfx=280\displaystyle \Sigma fx = 280 and σ(S.D.)=3\displaystyle \sigma(\text{S.D.}) = 3.
MCQ
4073
The monthly profit/loss for six months of the firm is as under: January ₹ 1,000, February ₹ 900, March ₹ 0, April ₹ -200, May ₹ -400, June ₹ 2,000. The co-efficient range of the above data is
MCQ
4074
Which one of the following is the absolute measure of dispersion for open ended distributions?
MCQ
4075
If the mean of the following frequency distribution is 2.6, then the value of Y is: Marks (X): 1, 2, 3, 4, 5. No. of Students (f): 8, 10, Y, 2, 4
MCQ
4076
Which one of the following measures of central tendency is based on only fifty percent (50%) of the central values?
MCQ
4077
The Arithmetic Mean (A.M.) and mode of the data are 32 and 26, respectively, then find the median of the data.
MCQ
4078
Find out the mode from the following data: 100, 110, 125, 225, 325, 125, 90, 80, 455, 375, 125
MCQ
4169
If X\displaystyle X and Y\displaystyle Y are related by 4X+3Y+5=0\displaystyle 4X+3Y+5=0 and Mean of X\displaystyle X is 10, then the Mean of Y\displaystyle Y is
MCQ
4170
For a moderately skewed distribution of marks in English for a group of 145 students the mean marks and median marks were found to be 55.10 and 52.40, respectively. The modal marks are -
MCQ
4171
If there are two groups with 10 and 12 observations and harmonic mean of the two groups are 3 and 5 respectively, then the combined Harmonic mean is
MCQ
4172
Best measure of Dispersion for open-end classification is the _______, which does not change with the change of _________.
MCQ
4173
Coefficient of range of 84, 93, 53, 70, 82, 65 is
MCQ
4174
Calculate the Harmonic Mean of 1\displaystyle 1, 13\displaystyle \frac{1}{3}, 16\displaystyle \frac{1}{6} and 19\displaystyle \frac{1}{9}
MCQ
4175
Find the Coefficient of variation for the following numbers; 7, 5, 9, 3, 6
MCQ
4176
A set contains seven numbers whose average is 12. The average of four greater numbers is 18 and the average of four smaller numbers is 8. Which of the followings is the value of one of the numbers?
MCQ
4177
If the sum of ten values is 20 and sum of squares of these values is 80, then the standard deviation is
MCQ
4178
A data set has first eleven positive multiples of 6. The semi inter-quartile range is
MCQ
4213
If the arithmetic mean of two numbers is 13 and the geometric mean is 12, then the difference between the two numbers is:
MCQ
4233
In two groups, unit one has 700 people with monthly salary of ₹ 2,500, unit two has 650 with salary of ₹ 2,750 then approximate combined arithmetic mean with monthly salary (in ₹) is
MCQ
4234
If the relationship between x and y is given by 5x−3y=15\displaystyle 5x - 3y = 15 and if range of x is given as 24 then the range of y is given by:
MCQ
4235
The two variables 'x' and 'y' are related by 2x−3y−3=0\displaystyle 2x - 3y - 3 = 0. If the mode of 'x' is 15, then the mode of 'y' is:
MCQ
4236
If mean of 5 observations x+1,x+3,x+5,x+7\displaystyle x+1, x+3, x+5, x+7 and x+9\displaystyle x+9 is given as 125, then the value of x will be.
MCQ
4237
If two samples of size 30 and 20 have means as 55 and 60 and standard deviation 5 and 6 respectively then what would be the standard deviation of combined sample of size 50?
MCQ
4284
If arithmetic mean of two numbers is 64 and harmonic mean is 16 then geometric mean is
MCQ
4285
In continuous frequency distribution, the median of the data is 32. If each observation is increased by 7, then the new median will be:
MCQ
4286
If mean is 21 and median is 25 then value of mode is
MCQ
4287
Calculate the coefficient of quartile deviation for 11, 55, 65, 22, 33, 98, 88
MCQ
4288
If two variables 'x' and 'y' are related by 3x+4y−7=0\displaystyle 3x + 4y - 7 = 0 and mean & mean deviation about mean of 'x' are 1.2 and 0.4 respectively then the coefficient of mean deviation of 'y' about its mean is?
MCQ
2879
The mean salary for a group of for a group of 50 male workers is Rs.4800 per month and that for a group of 50 female workers is Rs. 5600. the combined mean salary is
MCQ
2863
There are n\displaystyle n numbers. When 50 is subtracted from each of these number the sum of the numbers so obtained is −10\displaystyle -10. When 46 is subtracted from each of the original n\displaystyle n numbers, then the sum of numbers so obtained is 70. What is the mean of the original n\displaystyle n numbers?
MCQ
2884
The mean of four observations is 10 and when a constant a is added to each observation, the mean becomes 13. The value of a is
MCQ
2897
The sum of mean and SD of a series is a+b\displaystyle a+b, if we add 2 to each observations of the series then the sum of the mean and SD is
MCQ
3013
If there are two groups with 75\displaystyle 75 and 65\displaystyle 65 as harmonic means containing 15\displaystyle 15 and 13\displaystyle 13 observation, then combined HM is given by
MCQ
3127
Which of the below is affected by shifting of scale.
MCQ
3203
If the S.D. of x\displaystyle x is 4\displaystyle 4, what is the variance of (5−2x)\displaystyle (5 - 2x)?
MCQ
2908
A batsman in his 20th\displaystyle 20^{th} innings makes a score of 120\displaystyle 120 and thereby increases his average by 5\displaystyle 5. What is his average after 20th\displaystyle 20^{th} innings?
MCQ
3053
For a moderately skewed distribution, which of the following relationship holds?
MCQ
3074
If the range of a set of values is 65\displaystyle 65 and maximum value in the set is 83\displaystyle 83, then the minimum value in the set is
MCQ
3155
If the profits of a company remain the same for the last ten months, then the standard deviation of profits for these ten months would be?
MCQ
2918
The average weight of 40\displaystyle 40 people is increased by 2.4\displaystyle 2.4 kg when one man weight 73\displaystyle 73 kg is replaced by another man. Find the weight of the new man?
MCQ
3166
The mean and SD for a,b,\displaystyle a, b, and 2\displaystyle 2 are 3\displaystyle 3 and 1\displaystyle 1 respectively, the value of ab\displaystyle ab would be
MCQ
2920
The average of 6\displaystyle 6 numbers is 30\displaystyle 30. If the average of the first four is 25\displaystyle 25 and that of the last three is 35\displaystyle 35, the fourth number is
MCQ
2994
If y=3+(4.5)x\displaystyle y = 3 + (4.5)x and the mode for x\displaystyle x - value is 20\displaystyle 20, then the mode for y\displaystyle y - value is
MCQ
3029
If the AM & GM of two numbers are 30\displaystyle 30 and 24\displaystyle 24 respectively. Find the no's.
MCQ
3075
Difference between upper limit and lower limit of a class is known as.
MCQ
2928
The average age of a group of 10\displaystyle 10 students was 20\displaystyle 20 years. The average age is increased by two years when two new students joined the group. What is the average age of two new students who joined the group ?
MCQ
3025
Relation between mean, median and mode is
MCQ
3064
For a moderately skewed distribution, which of the following relationship is correct
MCQ
3178
If all the observations are decreased by 4, find the relation between new SD and old SD.
MCQ
3221
Standard deviation is ________ times of MD×QD\displaystyle \sqrt{MD \times QD}
MCQ
3232
The Quartile Deviation of the distribution of the following data is:x123456f(x)224848\displaystyle \begin{array}{|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline f(x) & 2 & 2 & 4 & 8 & 4 & 8 \\ \hline \end{array}
MCQ
2999
If two variables a\displaystyle a and b\displaystyle b are related by c=ab\displaystyle c = ab then G.M. of c\displaystyle c is equal to
MCQ
3046
For a moderately-skewed distribution, which of the following relationship holds?
MCQ
3138
If the sum of square of the values equals to 3390, Number of observations are 30 and Standard deviation is 7, what is the mean value of the above observations?
MCQ
3173
If the profits of a company remains the same for the last ten months, then the standard deviation of profits for these ten months would be ?
MCQ
3004
Find the mode of the following data:X | F(x)25-30 | 2030-35 | 5335-40 | 4240-45 | 4245-50 | 4150-55 | 43
MCQ
3021
A shopkeeper wants to place an order for t-shirts with the wholesaler based on past sales data. The size he orders will be decided by looking at the ________ of past sales data?
MCQ
3148
The Standard Deviation of the series is 3,6,9,12,15\displaystyle 3, 6, 9, 12, 15 is:
MCQ
3176
The Standard Deviation of a variable x\displaystyle x is known to be 10. The Standard deviation of 50+5x\displaystyle 50+5x
MCQ
3220
Which is not a measure of central tendency
MCQ
3014
The Geometric mean of the series 1,k,k2,k3,...,kn\displaystyle 1, k, k^2, k^3, ..., k^n where k\displaystyle k is constant is
MCQ
3058
Which of the following is not a criteria for ideal measure of central tendency?
MCQ
3136
Find the standard deviation and coefficient of variation for 1,9,8,7,5\displaystyle 1, 9, 8, 7, 5.
MCQ
3204
Mean and S.D. of a given set of observations is 1,500\displaystyle 1,500 and 400\displaystyle 400 respectively. If there is an increment of 100\displaystyle 100 in the first year and each observation is hiked by 20%\displaystyle 20\% in 2\displaystyle 2nd years, then find new mean and S.D.
MCQ
3019
A train covered the first 5 km\displaystyle 5 \text{ km} of its journey at a speed of 30km/hr\displaystyle 30 \text{km/hr}, and the next 15 km\displaystyle 15 \text{ km} at a speed of 45km/hr\displaystyle 45 \text{km/hr}. The average speed of the train was:
MCQ
3049
The relationship between AM, GM, and Median
MCQ
3062
Which of the following is the correct relation between mean, median and mode
MCQ
3143
The mean and variance of a group of 100 observations are 8 and 9 respectively. Out of 100 observations, the mean and standard deviation of 60 observations are 10 and 2 respectively. Find the variance of remaining 40 observations?
MCQ
3217
The Q.D of 6\displaystyle 6 numbers 15,8,36,40,38,41\displaystyle 15, 8, 36, 40, 38, 41 is
MCQ
4369
A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is
MCQ
4370
If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are
MCQ
4371
Which of the following is not a method of dispersion?
MCQ
4372
Find out co-efficient of variation, if N=14\displaystyle N = 14, Σfx=280\displaystyle \Sigma fx = 280 and σ(S.D.)=3\displaystyle \sigma(\text{S.D.}) = 3.
MCQ
4373
The monthly profit/loss for six months of the firm is as under: January ₹ 1,000, February ₹ 900, March ₹ 0, April ₹ -200, May ₹ -400, June ₹ 2,000. The co-efficient range of the above data is
MCQ
4374
Which one of the following is the absolute measure of dispersion for open ended distributions?
MCQ
4375
If the mean of the following frequency distribution is 2.6, then the value of Y is: Marks (X): 1, 2, 3, 4, 5. No. of Students (f): 8, 10, Y, 2, 4
MCQ
4376
Which one of the following measures of central tendency is based on only fifty percent (50%) of the central values?
MCQ
4377
The Arithmetic Mean (A.M.) and mode of the data are 32 and 26, respectively, then find the median of the data.
MCQ
4378
Find out the mode from the following data: 100, 110, 125, 225, 325, 125, 90, 80, 455, 375, 125
MCQ
4469
If X\displaystyle X and Y\displaystyle Y are related by 4X+3Y+5=0\displaystyle 4X+3Y+5=0 and Mean of X\displaystyle X is 10, then the Mean of Y\displaystyle Y is
MCQ
4470
For a moderately skewed distribution of marks in English for a group of 145 students the mean marks and median marks were found to be 55.10 and 52.40, respectively. The modal marks are -
MCQ
4471
If there are two groups with 10 and 12 observations and harmonic mean of the two groups are 3 and 5 respectively, then the combined Harmonic mean is
MCQ
4472
Best measure of Dispersion for open-end classification is the _______, which does not change with the change of _________.
MCQ
4473
Coefficient of range of 84, 93, 53, 70, 82, 65 is
MCQ
4474
Calculate the Harmonic Mean of 1\displaystyle 1, 13\displaystyle \frac{1}{3}, 16\displaystyle \frac{1}{6} and 19\displaystyle \frac{1}{9}
MCQ
4475
Find the Coefficient of variation for the following numbers; 7, 5, 9, 3, 6
MCQ
4476
A set contains seven numbers whose average is 12. The average of four greater numbers is 18 and the average of four smaller numbers is 8. Which of the followings is the value of one of the numbers?
MCQ
4477
If the sum of ten values is 20 and sum of squares of these values is 80, then the standard deviation is
MCQ
4478
A data set has first eleven positive multiples of 6. The semi inter-quartile range is
MCQ
4513
If the arithmetic mean of two numbers is 13 and the geometric mean is 12, then the difference between the two numbers is:
MCQ
4533
In two groups, unit one has 700 people with monthly salary of ₹ 2,500, unit two has 650 with salary of ₹ 2,750 then approximate combined arithmetic mean with monthly salary (in ₹) is
MCQ
4534
If the relationship between x and y is given by 5x−3y=15\displaystyle 5x - 3y = 15 and if range of x is given as 24 then the range of y is given by:
MCQ
4535
The two variables 'x' and 'y' are related by 2x−3y−3=0\displaystyle 2x - 3y - 3 = 0. If the mode of 'x' is 15, then the mode of 'y' is:
MCQ
4536
If mean of 5 observations x+1,x+3,x+5,x+7\displaystyle x+1, x+3, x+5, x+7 and x+9\displaystyle x+9 is given as 125, then the value of x will be.
MCQ
4537
If two samples of size 30 and 20 have means as 55 and 60 and standard deviation 5 and 6 respectively then what would be the standard deviation of combined sample of size 50?
MCQ
4584
If arithmetic mean of two numbers is 64 and harmonic mean is 16 then geometric mean is
MCQ
4585
In continuous frequency distribution, the median of the data is 32. If each observation is increased by 7, then the new median will be:
MCQ
4586
If mean is 21 and median is 25 then value of mode is
MCQ
4587
Calculate the coefficient of quartile deviation for 11, 55, 65, 22, 33, 98, 88
MCQ
4588
If two variables 'x' and 'y' are related by 3x+4y−7=0\displaystyle 3x + 4y - 7 = 0 and mean & mean deviation about mean of 'x' are 1.2 and 0.4 respectively then the coefficient of mean deviation of 'y' about its mean is?
MCQ
3128
Coefficient of variation is 80\displaystyle 80. Mean is 20\displaystyle 20. Find variance:
MCQ
2998
Expenditures of a company (in million rupees) per item in various yearsYear | Item of expenditure| Salary | Fuel & Bonus | Int on | Taxes| | Wages | | Loans || 1998 | 288 | 98 | 3.00 | 23.4 | 83| 1999 | 342 | 112 | 3.50 | 32.5 | 108| 2000 | 324 | 108 | 3.84 | 41.6 | 74| 2001 | 336 | 123 | 3.68 | 36.4 | 88| 2002 | 420 | 142 | 3.96 | 49.4 | 98What is the avg. interest per year which the company had to pay during this period?
MCQ
3000
Given the weights for the numbers 1,2,3,…,n\displaystyle 1, 2, 3, \dots, n are respectively 12,22,32,…,n2\displaystyle 1^2, 2^2, 3^2, \dots, n^2 then weighted HM is
MCQ
3001
The harmonic mean A\displaystyle A and B\displaystyle B is 1/3\displaystyle 1/3 and harmonic mean of C\displaystyle C and D\displaystyle D is 1/5\displaystyle 1/5. The harmonic mean of ABCD\displaystyle ABCD is
MCQ
3002
A fire engine rushes to a place of fire accident with a speed of 110\displaystyle 110 kmph and after the completion of operation returned to the base at a speed of 55\displaystyle 55 kmph. The average speed per hour in per-direction is obtained as ________ speeds.
MCQ
3003
If there are two groups with n1\displaystyle n_1 and n2\displaystyle n_2 observations and H1\displaystyle H_1 and H2\displaystyle H_2 are respective harmonic means, then the harmonic mean of combined observation is
MCQ
3137
If the coefficient of variation and standard deviation are 30 and 12 respectively, then the arithmetic mean of the distribution is:
MCQ
3259
If Quartile deviation is 7\displaystyle 7. Find the value of x\displaystyle x from the arranged series: 2,x,6,7,9,16,18\displaystyle 2, x, 6, 7, 9, 16, 18.
MCQ
2965
Which of the following measure of central tendency depends on the position of the observation?
MCQ
2976
The median of data 13,8,11,6,4,15,2,18\displaystyle 13, 8, 11, 6, 4, 15, 2, 18 is
MCQ
3260
If the first quartile is 142\displaystyle 142 and semi-inter quartile range is 18\displaystyle 18, then the value of median is:
MCQ
3198
If the variance of given data is 12\displaystyle 12, and their mean value is 40\displaystyle 40, what is coefficient of variation (CV)?
MCQ
3208
The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their
MCQ
3218
Coefficient of quartile deviation is 1/4\displaystyle 1/4 then Q3/Q1\displaystyle Q_3 / Q_1
MCQ
3219
Which of the following is a relative measure of dispersion?
MCQ
2891
The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their:
MCQ
2892
Let the mean of the variable 'x\displaystyle x' be 50, then the mean of u=10+5x\displaystyle u=10+5x will be.
MCQ
3244
The quartiles of a variable are 45\displaystyle 45, 52\displaystyle 52 and 65\displaystyle 65 respectively. Its quartile deviation is
MCQ
2893
If sum of squares of the values = 3390, N = 30 and standard deviation = 7, find out the mean.
MCQ
2907
The mean weight of 15\displaystyle 15 students is 110\displaystyle 110 kg. The mean weight of 5\displaystyle 5 of them is 100\displaystyle 100 kg, and of another five students is 125\displaystyle 125 kg, then the mean weight of the remaining students is :
MCQ
2926
The average wages of a group of unexperienced labours is 1000\displaystyle 1000 and that of a group of experienced labours is 1,500\displaystyle 1,500. If the combined wage is 1200\displaystyle 1200, then what is the percentage of experienced labours?
MCQ
2927
If the arithmetic mean of 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 6n11\displaystyle \frac{6n}{11} then the value of 'n\displaystyle n' is:
MCQ
2937
The mean of first 3 terms is 14 and the mean of next 2 terms is 18. The mean of 5 numbers is -
MCQ
2894
Which of the following measures of central tendency cannot be calculated by graphical method?
MCQ
2895
The mean salary for a group of 40 female workers is 5000 per month and that for a group of 60 male workers is 6000 per month. What is the combined mean salary?
MCQ
2896
The mean of the variable x\displaystyle x is 50, then the mean of u=10+5x\displaystyle u=10+5x will be
MCQ
3258
In case of extreme sampling fluctuations, which is the best measure of dispersion?
MCQ
3154
If all the observations are multiplied by 2, then
MCQ
2861
The AM of 15 observation is 9 and the AM of first 9 observation is 11 and then AM of remaining observation is
MCQ
2862
∑(xi−xˉ)\displaystyle \sum (x_i - \bar{x}) is equal to
MCQ
3175
The Sum of the squares of the deviations from mean of 10 observations is 250. Mean of the data is 10. Find coefficient of variation.
MCQ
2880
The mean age of a group of 100 men and women is 25 years. If the mean age of the group of men is 26, then that of the group of women is 21 then the ratio of women and men in the group:
MCQ
2853
If the variables x\displaystyle x and z\displaystyle z are so related that z=ax+b\displaystyle z = ax+b for each where a\displaystyle a and b\displaystyle b are constant, then z=ax+b\displaystyle z = ax+b.
MCQ
2854
If each item is reduced by 15 A. M is
MCQ
2855
The average of a series of overlapping averages, each of which is based on a certain number of item within a series is know as.
MCQ
2856
The mean of 20 items of a data is 5 & if each item is multiplied by 3, then the new mean will be
MCQ
2857
The algebraic sum of the deviation of a set of values from their arithmetic mean is
MCQ
2858
Which one of the following is not a central tendency?
MCQ
2859
If total frequencies of three series are 50, 60 and 90 and their means are 12, 15 and 20 respectively, then the mean of their composite series is
MCQ
2860
If the mean of the following distribution is 6, then the value of P\displaystyle P is X | 2 | 4 | 6 | 10 | P+5 F | 3 | 2 | 3 | 1 | 2
MCQ
2864
The mean of 'n\displaystyle n' observation is 'x\displaystyle x'. If k\displaystyle k is added to each observation, then the new mean is.
MCQ
2865
If there are 3 observations 15, 20, 25 then sum of deviation of the observations from AM is
MCQ
2866
If average mark for a group of 30 girls is 80, a group of boys is 70 and combined average is 76, then how many are in the boy's group?
MCQ
2867
For a data having odd number of values, the difference between the first and the middle value is equal to the difference between the last and the middle value; similarly, the difference between the second and middle values is equal to that of second last and middle value so on. Therefore, the middle value is equal to
MCQ
2868
When each value does not have equal importance then we use
MCQ
2869
The mean of 20 observation is 38. If two observation are taken as 84 and 36 instead of 48 and 63 find new means.
MCQ
2870
The mean of 50 observations is 36. If two observations 30 and 42 are to be excluded, then the mean of the remaining observations will be:
MCQ
2890
Two variables assume the values 1,2,…,5\displaystyle 1, 2, \dots, 5 with frequencies as 1,2,3,…,5\displaystyle 1, 2, 3, \dots, 5 then what is the AM?
MCQ
2871
The average age of 15 students in a class is 9 years. Out of them, the average age of 5 students is 13 years and that 5 students is 8 years. What is the average of remaining 2 students?
MCQ
2872
A Professor has given assignment to students in a Statistics class. A student Jagan computes the arithmetic mean and standard deviation for a set of 100 observations as 50 and 5 respectively. Later on, Sonali points out to Jagan that he has made of mistake in taking one observation as 100 instead of 50. What would be the correct mean if the wrong observation is corrected?
MCQ
2873
Find the mean of the following data Class Interval | Frequency 10-20 | 9 20-30 | 13 30-40 | 20 40-50 | 14 50-60 | 6 60-70 | 4 70-80 | 2
MCQ
2874
The mean of a set of 20 observations is 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:
MCQ
2875
If mean of 5 observations x+1,x+3,x+5,x+7\displaystyle x+1, x+3, x+5, x+7 and x+9\displaystyle x+9 is given 15, then the value of x\displaystyle x will be:
MCQ
2876
The mean of the first three terms is 17 and mean of next four terms is 21. Calculate the mean of seven terms.
MCQ
2877
If there are two groups containing 40 and 30 observations and have arithmetic means as 50 and 60, then the combined arithmetic mean is
MCQ
2878
The mean of group X is 70 and the mean of group Y is 85. If the number of observations in group Y is five times that of group X, then the combined mean of both the group is:
MCQ
2881
If the relationship between two variables u\displaystyle u and v\displaystyle v are given by 2u+7v=0\displaystyle 2u + 7v = 0 and if the AM of u\displaystyle u is 10, then the AM of v\displaystyle v is
MCQ
2882
If there are 3 observations 15, 20, 25 then the sum of deviation of the observations from their AM is
MCQ
2883
The mean of the values of 1,2,3,…,n\displaystyle 1, 2, 3, \dots, n with respective frequencies x,2x,3x,…,nx\displaystyle x, 2x, 3x, \dots, nx is.
MCQ
2885
The average salary of a group of unskilled workers is Rs.10,000 and that of a group of skilled workers is Rs.15,000. If the combined salary is Rs.12,000, then what is the percentage of skilled workers?
MCQ
2886
The mean of first 3 terms is 14 and the mean of next 2 terms is 18. The mean of 5 numbers is
MCQ
2887
If the mean of the set of observations x1,x2,x3,…,xn\displaystyle x_1, x_2, x_3, \dots, x_n is xˉ\displaystyle \bar{x}, then the mean of the observation xi+ki\displaystyle x_i + ki, where i=1,2,3,…,n\displaystyle i = 1, 2, 3, \dots, n
MCQ
2888
The average of n\displaystyle n numbers is x\displaystyle x. If each of the numbers is multiplied by (n+1)\displaystyle (n+1), then the average of new set of numbers is
MCQ
2889
The average weight of 8 person increases by 1.5 kg, if a person weighing 65 kg replaced by a new person, what would be the weight of the new person?
MCQ
2898
At ABC Ltd, the average age of employees is 36. Average age of male employees is 38 and that of female is 32. Find the ratio of female to male in the company.
MCQ
2899
The mean height of girls in class in 162cm while for boys is 182cm. The ratio of no. of girls: boys is 1:2. Find the mean height of the whole class
MCQ
2900
The average of 10 observations is 14.4. If the average of first four observations is 16.5. The average of remaining 6 observations is:
MCQ
2901
Mean of 25,32,43,53,62,59,48,31,24,33 is
MCQ
2902
If the A.M of any distribution be 25 & one term is 18. Then the deviation of 18 from A.M is
MCQ
2903
The algebraic sum of the deviations of a frequency distribution from its mean is always,
MCQ
2904
Pooled Mean is also called
MCQ
2905
If average marks for a group of 30\displaystyle 30 girls is 80\displaystyle 80, a group of boys is 70\displaystyle 70 and combined average is 76\displaystyle 76, then how many boys are in the group ?
MCQ
2906
If there are three observations 15,20,25\displaystyle 15, 20, 25, then the sum of deviation of the observations from their AM is.
MCQ
2909
The mean of first three terms is 14\displaystyle 14 and mean of next two terms is 18\displaystyle 18. The mean of all five terms is
MCQ
2910
In a group of persons, average weight is 60\displaystyle 60 kg. If the average of males and females taken separately is 80\displaystyle 80 kg and 50\displaystyle 50 kg respectively, find the ratio of the number of males to that of females.
MCQ
2911
The mean of 100\displaystyle 100 students was 45\displaystyle 45. Later, it was discovered that the marks of two students were misread as 85\displaystyle 85 and 54\displaystyle 54 instead of 58\displaystyle 58 and 45\displaystyle 45. Find correct mean.
MCQ
2912
The AM of 15\displaystyle 15 observations is 9\displaystyle 9 and the AM of first 9\displaystyle 9 observations is 11\displaystyle 11 and then AM of remaining observations is:
MCQ
2913
The mean of 100\displaystyle 100 observations is 50\displaystyle 50. If one of the observations which was 50\displaystyle 50 is replaced by 40\displaystyle 40, the resulting mean will be:
MCQ
2914
The mean annual salary of all employees in a company is 25,000\displaystyle 25,000. The mean salary of male and female employees is 27,000\displaystyle 27,000 and 17,000\displaystyle 17,000 respectively. Find the percentage of males and females employed by the company.
MCQ
2915
The average age of 15\displaystyle 15 numbers in a class is 9\displaystyle 9 years. Out of them, the average age of 5\displaystyle 5 students is 13\displaystyle 13 years and that of 8\displaystyle 8 students is 5\displaystyle 5 years. What is the average of remaining 2\displaystyle 2 students?
MCQ
2916
The students of a class 10th\displaystyle 10^{th} have an average weight of 50\displaystyle 50 kg. The strength of the class is 49\displaystyle 49 students. On including the weight of the principal, the average weight shoots up by 0.8\displaystyle 0.8 kg. Find the weight of the principal?
MCQ
2917
The average of 'r\displaystyle r' consecutive numbers starting from 1\displaystyle 1 is 'r\displaystyle r'. If 2\displaystyle 2 is added to each of the number. Then the new average will be?
MCQ
2919
The average salary of the whole employees in a company is 400\displaystyle 400 per day. The average salary of officers is 800\displaystyle 800 per day and that of clerks is 320\displaystyle 320 per day. If the number of officers is 40\displaystyle 40, then find the number of clerks in the company?
MCQ
2921
A student marks were wrongly entered as 85\displaystyle 85 instead of 45\displaystyle 45. Due to that the average marks for the whole class got increased by one-fourth. The no. of students in the class is?
MCQ
2922
The mean salary of a group of 50\displaystyle 50 persons is Rs. 5850\displaystyle 5850. Later on it is discovered that the salary of one has been wrongly taken as Rs. 8000\displaystyle 8000 instead of Rs. 7500\displaystyle 7500. The corrected mean salary is
MCQ
2923
The algebraic sum of the deviations of set of values from their arithmetic mean is
MCQ
2924
The AM of 15\displaystyle 15 observations is 9\displaystyle 9 and the AM of first 9\displaystyle 9 observations is 11\displaystyle 11 and then AM of remaining observations is
MCQ
2925
The weighted mean of first n\displaystyle n natural numbers, if their weights are proportional to their corresponding numbers is
MCQ
2929
There were 50\displaystyle 50 students in a class. 10\displaystyle 10 failed whose average marks were 2.5\displaystyle 2.5. The total marks of class were 281\displaystyle 281. Find the average marks of students who passed?
MCQ
2930
When 10\displaystyle 10 is subtracted from all the observations, the mean is reduced to 60%\displaystyle 60\% of its value. If 5\displaystyle 5 is added to all the observations, then the mean will be
MCQ
2931
The mean salary for a group of 40\displaystyle 40 female workers is 5200\displaystyle 5200 per month and that for a group of 60\displaystyle 60 male workers is 6800\displaystyle 6800 per month. What is the combined salary ?
MCQ
2932
The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg, and that of another five students is 125 kg., then the mean weight of the remaining students is:
MCQ
2933
The average age of 15 students is 15 years. Out of these the average age of 5 students is 14 years and that of other 9 students is 16 years, then the age of 15th student is ____.
MCQ
2934
The average of marks obtained by 120 students in a certain examination is 35. If the average marks of passed students is 39 and that of the failed students is 15, what is the number of students who passed in the examination?
MCQ
2935
The mean of the values of 1,2,3,…,n\displaystyle 1, 2, 3, \dots, n with respective frequencies x,2x,3x,…,nx\displaystyle x, 2x, 3x, \dots, nx is
MCQ
2936
Two variables x\displaystyle x and y\displaystyle y are related by 5x+2y+5=0\displaystyle 5x + 2y + 5 = 0 and x=10\displaystyle x = 10. If y\displaystyle y is
MCQ
2938
The Mean of a set of 20 observations on 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:
MCQ
2939
The mean salary of a group of 50 persons is ₹5850\displaystyle ₹5850. Later on it is discovered that the salary of one has been wrongly taken as ₹8000\displaystyle ₹8000 instead of ₹7800\displaystyle ₹7800. The corrected mean salary is:
MCQ
2940
The algebraic sum of the deviations of set of values from their arithmetic mean is:
MCQ
2941
The AM of 15 observations is 9 and the AM of first 9 observations is 11 and then AM of remaining observations is
MCQ
2942
Which one of these is least affected by extreme value?
MCQ
2943
Ten matches data is given. Then which of the following cannot be found?
MCQ
2944
Which of the following measure does not possess mathematical properties?
MCQ
2945
The median value of the set of observations 48,36,72,87,19,66,56,91\displaystyle 48, 36, 72, 87, 19, 66, 56, 91 is
MCQ
2964
Which of the following measure of central tendency will be unaffected if the lowest and highest observation are removed?
MCQ
2946
Along a road there are 5 buildings of apartments, marked as 1,2,3,4,5\displaystyle 1, 2, 3, 4, 5. Number of people residing in each building is available. A bus stop is to be setup near one of the buildings so that the total distance walked by the resident to the bus stop from their buildings must be kept minimum. One must consider investing ________ to find the position of the bus stop.
MCQ
2947
The 3rd\displaystyle 3^{rd} decile for the numbers 15,10,20,25,18,11,9,12\displaystyle 15, 10, 20, 25, 18, 11, 9, 12 is
MCQ
2948
The relationship between two variables x\displaystyle x and y\displaystyle y is given by 4x−10y=20\displaystyle 4x - 10y = 20. If the median value of the variable x\displaystyle x is 10 then what is median value of variable y\displaystyle y?
MCQ
2949
For 899,999,391,384,390,480,485,760,111,240\displaystyle 899, 999, 391, 384, 390, 480, 485, 760, 111, 240. Rank of median
MCQ
2950
The median of the data 5,6,7,8,9,10,11,12,15,18\displaystyle 5, 6, 7, 8, 9, 10, 11, 12, 15, 18, and 19\displaystyle 19 is
MCQ
2951
Which of the following is positional average?
MCQ
2952
For the distribution, The value of median is x: 1, 2, 3, 4, 5, 6; f: 6, 9, 10, 14, 12, 8
MCQ
2953
The deviations are minimum taken from:
MCQ
2954
Find the median of the following. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Freq: 2, 3, 4, 5, 6
MCQ
2955
Find the median of the following. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Freq: 5, 8, 15, 10, 2
MCQ
2956
Which measure is suitable for open-end classification?
MCQ
2957
50th\displaystyle 50^{th} Percentile is equal to
MCQ
2958
Mean deviation is minimum when deviations are taken from:
MCQ
2959
The median of the observations 42,72,35,92,67,85,72,81,51,56\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 56 is:
MCQ
2960
The median of the following set of observation: 24,18,36,42,30,28,21,29,25,33\displaystyle 24, 18, 36, 42, 30, 28, 21, 29, 25, 33 is
MCQ
2961
For a given data set: 5,10,3,6,4,8,9,3,15,2,9,4,19,11,4\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4, what is the median?
MCQ
2962
The median of the following frequency distribution is x | f(x) 0-10 | 5 10-20 | 8 20-30 | 20 30-40 | 12 40-50 | 7
MCQ
2963
If two variable 'x\displaystyle x' and 'y\displaystyle y' are related as 2x−y=3\displaystyle 2x - y = 3. If the median of 'x\displaystyle x' is 10\displaystyle 10, what is median of 'y\displaystyle y'?
MCQ
2966
The median of the following frequency distribution is: x | f(x) 0-10 | 8 10-20 | 30 20-30 | 40 30-40 | 12 40-50 | 10
MCQ
2967
For open-end classification, which of the following is the best measure of central tendency?
MCQ
2968
The presence of extreme observations does not affect
MCQ
2969
Quartiles are the values dividing a given set of observations into
MCQ
2970
What is the value of the first quartile for observations 15,18,10,20,23,28,12,16\displaystyle 15, 18, 10, 20, 23, 28, 12, 16?
MCQ
2971
The third decile for the numbers 15,10,20,25,18,11,9,12\displaystyle 15, 10, 20, 25, 18, 11, 9, 12 is
MCQ
2972
Two variables x\displaystyle x and y\displaystyle y are given by y=2x−3\displaystyle y = 2x - 3. If the median of x\displaystyle x is 20\displaystyle 20, what is the median of y\displaystyle y?
MCQ
2973
In case of an even number of observations which of the following is median?
MCQ
2974
Quartile can be determined graphically using
MCQ
2975
The point of intersection of less than ogive and greater than ogive curve is gives us
MCQ
2977
Find D6\displaystyle D_6 for the following observations. 7,9,5,4,10,15,14,18,6,20\displaystyle 7, 9, 5, 4, 10, 15, 14, 18, 6, 20
MCQ
2978
The median of 27,30,26,44,42,51,37\displaystyle 27, 30, 26, 44, 42, 51, 37 is
MCQ
2979
The median value of the set of observations 48,36,72,87,19,66,56\displaystyle 48, 36, 72, 87, 19, 66, 56 and 91\displaystyle 91
MCQ
2980
The first Quartile is 142\displaystyle 142 and Semi-inter Quartile Range is 18\displaystyle 18, then the value of Median is:
MCQ
2981
Calculate the value of 3rd quartile from the following data 40,35,51,21,25,16,29,27,32\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 32
MCQ
2982
For the distribution, calculate MedianX | 1 | 2 | 3 | 4 | 5 | 6F | 6 | 9 | 10 | 14 | 12 | 8
MCQ
2983
The relationship between two variable x\displaystyle x and y\displaystyle y is given by 4x−10y=20\displaystyle 4x - 10y = 20. If the median value of the variable x\displaystyle x is 20\displaystyle 20 then what is median value of variable y\displaystyle y?
MCQ
2984
The median of the observations 42,72,35,92,67,85,72,81,51,56\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 56 is
MCQ
2985
The median of following numbers, which are given in ascending order is x,25,30,35,39,46,x+1,13,15,19,(x+2),(x+4),30,35,39,46\displaystyle x, 25, 30, 35, 39, 46, x+1, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46.
MCQ
2986
The third decile for the numbers 35,10,20,25,18,11,12\displaystyle 35, 10, 20, 25, 18, 11, 12 and 12\displaystyle 12 is
MCQ
2987
If the relationship between x\displaystyle x and y\displaystyle y is 4x−6y=13\displaystyle 4x - 6y = 13 & median of x\displaystyle x is 16\displaystyle 16. Find median of y\displaystyle y.
MCQ
2988
Find Q1\displaystyle Q_1 for the following observations: 7,9,5,4,10,15,14,18,6,20\displaystyle 7,9,5,4,10,15,14,18,6,20
MCQ
2989
The wages of 8\displaystyle 8 workers expressed in rupees are 42,45,49,38,56,54,55,47\displaystyle 42,45,49,38,56,54,55,47. Find median wage?
MCQ
2990
Find the mode of the following data:Class | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-21Freq. | 2 | 5 | 10 | 23 | 21 | 12
MCQ
2991
Histogram is used to represent
MCQ
2992
Find the mode of the following:0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-607 | 14 | 22 | 34 | 20 | 19
MCQ
2993
From the record on sizes of shoes sold in a shop, one can compute the following to determine the most preferred shoe size.
MCQ
2995
If y=3+1.9x\displaystyle y = 3 + 1.9x, and mode of x\displaystyle x is 15\displaystyle 15, then the mode of y\displaystyle y is:
MCQ
2996
One hundred participants expressed their opinion on recommending a new product to their friends using the attributes : most unlikely, not sure, likely, most likely. The appropriate measure of central tendency that can be used here is
MCQ
2997
The Geometric mean of 3,6,24\displaystyle 3, 6, 24 and 48\displaystyle 48 is
MCQ
3005
Geometric Mean of 3,7,11,15,24,28,30,0\displaystyle 3, 7, 11, 15, 24, 28, 30, 0 is
MCQ
3006
If the arithmetic mean of two numbers is 10\displaystyle 10 and the geometric mean is 6\displaystyle 6, then the difference in the numbers is
MCQ
3007
If two variables a\displaystyle a and b\displaystyle b are related by c=ab\displaystyle c = ab then GM. of c\displaystyle c =
MCQ
3008
Geometric Mean of 8,4,2\displaystyle 8, 4, 2 is
MCQ
3009
The geometric mean of the numbers 40,50\displaystyle 40, 50, and x\displaystyle x is 10\displaystyle 10, and the value of x\displaystyle x is
MCQ
3010
A man travels from Delhi to Agra at an average speed of 30km per hour\displaystyle 30 \text{km per hour} and back at an average speed of 60km per hour\displaystyle 60 \text{km per hour}. What's the average speed.
MCQ
3011
If x\displaystyle x and y\displaystyle y are related by x−y−10=0\displaystyle x - y - 10 = 0 and mode of x\displaystyle x is known to be 23\displaystyle 23, then the mode of y\displaystyle y is
MCQ
3012
A person travels from A to B at the rate of 20 km/hr\displaystyle 20 \text{ km/hr} and from B to A at the rate of 30 km/hr\displaystyle 30 \text{ km/hr}. What is the average rate of whole journey?
MCQ
3041
If A.M and G.M of two positive numbers a\displaystyle a and b\displaystyle b are 12 and 12, respectively, find the numbers
MCQ
3015
A man travels at a speed of 20km/hr\displaystyle 20 \text{km/hr} and then returns at a speed of 30km/hr\displaystyle 30 \text{km/hr}. His average speed of the whole journey is:
MCQ
3016
G.M is a better measure than others when,
MCQ
3017
If there are two groups with 75\displaystyle 75 and 65\displaystyle 65 as harmonic means and containing 15\displaystyle 15 and 13\displaystyle 13 observations. Then the combined H.M. is given by:
MCQ
3018
If there are two groups with 75\displaystyle 75 and 65\displaystyle 65 as harmonic means and containing 15\displaystyle 15 and 13\displaystyle 13 observations, then the combined HM is given by
MCQ
3020
Mode is:
MCQ
3022
The Harmonic mean H of two numbers is 4\displaystyle 4 and their arithmetic means A\displaystyle A and the geometric mean G\displaystyle G satisfy eq. 2A+G2=27\displaystyle 2A + G^2 = 27, the numbers are
MCQ
3023
The harmonic mean of 1,1/2,1/3,...,1/n\displaystyle 1, 1/2, 1/3, ..., 1/n is
MCQ
3024
The rate of returns from three different shares are 100%,200%\displaystyle 100\%, 200\% and 400%\displaystyle 400\% respectively. The average rate of return will be.
MCQ
3026
If in a moderately skewed distribution, the values of mode and mean are 32.1\displaystyle 32.1 and 35.4\displaystyle 35.4 respectively, then the value of the median is
MCQ
3027
In a moderately skewed distribution the values of mean & median are 12\displaystyle 12 & 8\displaystyle 8 respectively. The value of mode is
MCQ
3028
For a symmetric distribution
MCQ
3042
If the mean and median of a moderately asymmetrical series are 26.8 and 27.9 respectively, then the most probable mode is:
MCQ
3030
If the AM and HM of two numbers are 6\displaystyle 6 and 9\displaystyle 9 respectively, then GM is
MCQ
3031
If the AM and GM for 10 observations are both 15, then the value of HM is
MCQ
3032
For a moderately skewed distribution, the median is twice the mean, then mode is _times the median.
MCQ
3033
Given that mean = 70.20 and mode = 70.50, the Median is expected to be.
MCQ
3034
If Mean (X\displaystyle X) is = 10 and mode (Z\displaystyle Z) is = 7, then find out the value of median (M\displaystyle M).
MCQ
3035
If Arithmetic Mean and Geometric Mean between two numbers are 5 and 4 respectively, then these two numbers are:
MCQ
3036
If Arithmetic mean between two numbers is 5 and Geometric mean is 4 then what is the value of Harmonic mean?
MCQ
3037
For a moderately skewed distribution of marks in statistics for a group of 200 students, the mean marks and median marks are 55.60 and 52.40, respectively. What are the modal marks?
MCQ
3038
If the mean of two numbers is 30 and geometric mean is 24, then what will be the Harmonic mean of two numbers?
MCQ
3039
The AM and HM of two numbers are 5 and 3.2 respectively, then GM will be:
MCQ
3040
If mode of a grouped data is 10 and median is 6, then what is the value of mean?
MCQ
3043
If Mean of a data set is 22 and Median is 22.33 then Mode is
MCQ
3044
According to the empirical rule, if the data form a "bell-shaped" distribution, then the maximum and minimum frequencies occur at ______ and ______ respectively.
MCQ
3045
If the mean and median of a moderately asymmetrical series are 70.8 and 68.6 respectively, then the most probable mode is:
MCQ
3047
If the arithmetic mean between two numbers is 64\displaystyle 64 and the Geometric Mean between them is 16\displaystyle 16. The Harmonic mean between them is ______.
MCQ
3048
When the mean is 3.57 and mode is 2.13, then the value of median is ______.
MCQ
3050
Relationship between AM, GM, and HM
MCQ
3051
For a moderately skewed distribution, which is true
MCQ
3052
Which of the following results hold for a set of distinct positive observations?
MCQ
3054
If the A.M. and H.M. for two numbers are 5 and 3.2 respectively then the G.M. will be:
MCQ
3055
Which of the following statements is true?
MCQ
3056
When mean is 3.57 and mode is 2.13 then the value of the median is
MCQ
3057
The A.M and H.M for two numbers are 5 and 3.2 respectively then the G.M will be
MCQ
3059
If the rates return from three different shares are 100%\displaystyle 100\%, 200%\displaystyle 200\% and 400%\displaystyle 400\% respectively. The average rate of return will be.
MCQ
3060
Find the two numbers if AM and GM is 10\displaystyle 10 and 6\displaystyle 6 respectively.
MCQ
3061
For moderately skewed distribution, the median is twice the mean, then mode is \_ times the median.
MCQ
3085
If Rx\displaystyle R_x and Ry\displaystyle R_y denote ranges of x\displaystyle x and y\displaystyle y respectively where x\displaystyle x and y\displaystyle y are related by 3x+2y+10=0\displaystyle 3x+2y+10=0, what would be the relation between x\displaystyle x and y\displaystyle y?
MCQ
3063
If the mode of a data is 18\displaystyle 18 and mean is 24\displaystyle 24, then median is
MCQ
3065
The mode of data is 18\displaystyle 18 and mean is 24\displaystyle 24, then median is
MCQ
3066
Find the numbers whose GM is 5\displaystyle 5 and AM is 7.5\displaystyle 7.5:
MCQ
3067
If the difference between mean and mode is 69\displaystyle 69, then the difference between Mean and Median will be _______.
MCQ
3068
Which of the following result hold for a set of distinct positive observations?
MCQ
3069
______ & ______ are called ratio averages:
MCQ
3070
The Arithmetic Mean between two numbers is 15\displaystyle 15 and their G.M. is 9\displaystyle 9; then the numbers are −\displaystyle -
MCQ
3071
If the arithmetic mean between two numbers is 64\displaystyle 64 and the Geometric Mean between them is 16\displaystyle 16. The Harmonic mean between them is
MCQ
3072
When the mean is 3.57\displaystyle 3.57 and mode is 2.13\displaystyle 2.13, then the value of median is _______.
MCQ
3073
The HM, H\displaystyle H of two numbers is 4\displaystyle 4 and their AM, A\displaystyle A and the GM, G\displaystyle G satisfy the equation 2A+G2=27\displaystyle 2A+G^2=27, the numbers are:
MCQ
3076
The relationship between P-series and Q-series is given by 2P−3Q−10=0\displaystyle 2P - 3Q - 10 = 0. If the range of P-series is 18\displaystyle 18. What would be the range of Q?
MCQ
3077
If the relationship between x\displaystyle x and y\displaystyle y is given by 2x+3y=10\displaystyle 2x + 3y = 10 and the range of y\displaystyle y is 10\displaystyle 10, then what is the range of x\displaystyle x?
MCQ
3078
The marks secured by 5\displaystyle 5 students in a subject are 82,73,69,84,66\displaystyle 82, 73, 69, 84, 66. What is the coefficient of Range?
MCQ
3079
If the range of data is 20\displaystyle 20 and its smallest value is 5\displaystyle 5, then what is the largest value of data is?
MCQ
3080
What is the coefficient of range for the observations 20,28,32,41,48,50\displaystyle 20, 28, 32, 41, 48, 50?
MCQ
3081
What is the range of a data set?
MCQ
3082
If the range of x\displaystyle x is 2\displaystyle 2, find range of −3x+50\displaystyle -3x + 50?
MCQ
3083
The range of the 15,12,10,9,17,20\displaystyle 15, 12, 10, 9, 17, 20 is
MCQ
3084
The range of 15,12,10,9,17,30\displaystyle 15, 12, 10, 9, 17, 30 is
MCQ
3087
What is the coefficient of range for below: Class | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 Freq. | 11 | 25 | 16 | 7 | 3
MCQ
3088
Which of the following is a correct statement?
MCQ
3089
If Rx\displaystyle R_x and Ry\displaystyle R_y denote ranges of x\displaystyle x and y\displaystyle y respectively where x\displaystyle x and y\displaystyle y are related by 4x+5y+12=0\displaystyle 4x+5y+12=0, what would be the relation between Rx\displaystyle R_x and Ry\displaystyle R_y?
MCQ
3090
________ is an absolute measure of dispersion.
MCQ
3091
Which of the following measure of dispersion is based on absolute deviations?
MCQ
3092
Find the coefficient of mean deviation for mean for the data: 5,7,8,10,11,13,19\displaystyle 5, 7, 8, 10, 11, 13, 19
MCQ
3093
If a school has 14\displaystyle 14 teachers, their heights (in cm) are: 172,173,164,178,168,169,173,172,173,164,178,168,169,173\displaystyle 172, 173, 164, 178, 168, 169, 173, 172, 173, 164, 178, 168, 169, 173 then average deviation of this data is:
MCQ
3094
The probable value of mean deviation when Q3=40\displaystyle Q_3 = 40 and Q1=15\displaystyle Q_1 = 15 is:
MCQ
3095
If every observation is increased by 7\displaystyle 7 then:
MCQ
3096
The mean deviation of the numbers 3,10,6,11,14,17,9,8,12\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 12 about the mean is:
MCQ
3097
Mean Deviation of data 3,10,10,4,7,18,5\displaystyle 3, 10, 10, 4, 7, 18, 5 from mode is
MCQ
3098
Which of the below is based on absolute deviation?
MCQ
3099
If x\displaystyle x and y\displaystyle y are related as 4x+3y+11=0\displaystyle 4x+3y+11=0 and mean deviation of y\displaystyle y is 7.20\displaystyle 7.20, what is the mean deviation of x\displaystyle x?
MCQ
3100
The mean deviation about the mean for the data 12,16,24,30,35,39,40\displaystyle 12, 16, 24, 30, 35, 39, 40 is
MCQ
3101
If Mean deviation of Arithmetic Mean is 1.78\displaystyle 1.78 and Arithmetic Mean is 3.50\displaystyle 3.50 then coefficient of Mean deviation about Arithmetic mean is
MCQ
3102
The MD about the Mean for the data 6,9,11,10,12\displaystyle 6,9,11,10,12 is
MCQ
3103
The mean deviation about Mode for the numbers 4/11,6/11,8/11,9/11,12/11,8/11\displaystyle 4/11, 6/11, 8/11, 9/11, 12/11, 8/11 is
MCQ
3104
If the relation between x\displaystyle x and y\displaystyle y is 5y−3x=10\displaystyle 5y - 3x = 10 and the mean deviation about mean for x\displaystyle x is 12\displaystyle 12, then the mean deviation of y\displaystyle y about mean is
MCQ
3105
If two variables x\displaystyle x and y\displaystyle y are related by 2x+3y=0\displaystyle 2x + 3y = 0 and the mean and mean deviation about mean of x\displaystyle x are 1\displaystyle 1 and 0.3\displaystyle 0.3 respectively, then the co-efficient of mean deviation of y\displaystyle y about mean is:
MCQ
3106
The equation of a line is 5x+2y=17\displaystyle 5x + 2y = 17. Mean deviation of y\displaystyle y about mean is 5\displaystyle 5. Calculate mean deviation of x\displaystyle x about mean.
MCQ
3107
The deviations are minimum when taken from
MCQ
3108
The sum of squares of the deviations of the given values from their ................. is minimum.
MCQ
3109
Which measure of dispersion is based on the absolute deviation only?
MCQ
3110
Find the mean deviation about mean for the numbers: 2,6,7,4,8,3\displaystyle 2, 6, 7, 4, 8, 3
MCQ
3111
If the relation between x\displaystyle x and y\displaystyle y is 4y−3x=10\displaystyle 4y - 3x = 10 and the mean deviation about mean for x\displaystyle x is 12\displaystyle 12, then the mean deviation of y\displaystyle y about mean is
MCQ
3112
If two variables x\displaystyle x and y\displaystyle y are related by 2x+3y−7=0\displaystyle 2x + 3y - 7 = 0 and the mean and mean deviation about mean of X\displaystyle X are 1\displaystyle 1 and 0.3\displaystyle 0.3 respectively, then the co-efficient of mean deviation of Y\displaystyle Y about mean is.
MCQ
3113
The relation between two variables is 2x−3y+12=0\displaystyle 2x - 3y + 12 = 0 If mean deviation of y\displaystyle y is 6\displaystyle 6 then mean deviation of x\displaystyle x is
MCQ
3114
If two variables x\displaystyle x and y\displaystyle y are related by 2x\displaystyle 2x and 3y−7=0\displaystyle 3y - 7 = 0 and the mean and mean deviation about mean of x\displaystyle x are 1\displaystyle 1 and 0.3\displaystyle 0.3 respectively, then the coefficient of mean deviation of y\displaystyle y about mean is:
MCQ
3117
Standard Deviation for the marks obtained by a student in monthly test in mathematic (out of 50\displaystyle 50) as 30,35,25,20,15\displaystyle 30, 35, 25, 20, 15 is
MCQ
3118
If the standard deviation for the marks obtained by a student in monthly test is 36\displaystyle 36, then variance is
MCQ
3119
If σ2=100\displaystyle \sigma^2 = 100 & coefficient of variation =20%\displaystyle = 20\% then x\displaystyle x
MCQ
3120
S.D of first five consecutive natural numbers is
MCQ
3121
If the profits of a company remain some for the last ten months then the S.D. of profits of the company would be:
MCQ
3122
The sum of mean and SD of a series is a+b\displaystyle a + b, if we add 2\displaystyle 2 to each observation of the series then the sum of mean and SD is
MCQ
3123
Origin is shifted by 5\displaystyle 5, what will happen
MCQ
3124
Coefficient of variation is equal to:
MCQ
3125
Find SD of the following 1,2,3,4,5,6,7,8,9.\displaystyle 1, 2, 3, 4, 5, 6, 7, 8, 9.
MCQ
3126
If mean =200\displaystyle = 200 and variance =80\displaystyle = 80. Find coefficient of variation.
MCQ
3129
SD from numbers 1,4,5,7,8\displaystyle 1, 4, 5, 7, 8 is 2.45\displaystyle 2.45. If 10\displaystyle 10 is added to each then SD will be:
MCQ
3130
The best statistical measure used for comparing two series is
MCQ
3131
It is given that the mean (X\displaystyle X) is 10 and standard deviation (s.d.) is 3.2. If the observations are increased by 4, then the new mean and standard deviations are:
MCQ
3132
The SD of 1 to 9 natural number is:
MCQ
3133
If the numbers are 5,1,8,7,2\displaystyle 5, 1, 8, 7, 2 then the coefficient of variation is:
MCQ
3134
AM and Coefficient of variation of x\displaystyle x is 10 and 40. What is the variance 30−2x\displaystyle 30-2x?
MCQ
3135
Following are the wages of 8 workers 82,96,52,75,70,65,50,70\displaystyle 82, 96, 52, 75, 70, 65, 50, 70. Find range and coefficient of range?
MCQ
3139
If the variance of random variable 'x\displaystyle x' is 17, then what is variance of y=2x+5\displaystyle y = 2x+5?
MCQ
3140
If the variance of given data is 12, and their mean value is 40, what is coefficient of variation (CV)?
MCQ
3141
In a given set if all data are of same value then variance would be:
MCQ
3142
If the Standard Deviation of data 2,4,5,6,8,17\displaystyle 2, 4, 5, 6, 8, 17 is 4.47\displaystyle 4.47, then Standard Deviation of the data 4,8,10,12,16,34\displaystyle 4, 8, 10, 12, 16, 34 is
MCQ
3144
For the first 20 natural numbers the standard deviation is ________.
MCQ
3145
If Arithmetic mean and Coefficient of variations of x\displaystyle x are 5 and 20 respectively, the variance of 12−3x\displaystyle 12-3x is
MCQ
3146
Consider the data sets: X=[−6,2,−2,6]\displaystyle X = [-6, 2, -2, 6], Y=[4,8,2,6]\displaystyle Y = [4, 8, 2, 6] Z=[103,100,102,101]\displaystyle Z = [103, 100, 102, 101] Let SX,SY,SZ\displaystyle S_X, S_Y, S_Z be the standard deviations of the sets X,Y\displaystyle X, Y and Z\displaystyle Z respectively. We have the relations,
MCQ
3147
If each observation of a set is divided by 10, then the Standard Deviation of the new observation is:
MCQ
3149
If the mean of frequency distribution is 100 and coefficient of variation is 45%\displaystyle 45\%, then Standard deviation is
MCQ
3150
If the mean and SD of X\displaystyle X are a\displaystyle a and b\displaystyle b respectively, then the S.D of X=X−ab\displaystyle X = \frac{X-a}{b} is
MCQ
3151
Coefficient of Variation (CV) is calculated
MCQ
3152
The SD for the data 6,9,10,3,7\displaystyle 6, 9, 10, 3, 7 is
MCQ
3153
The standard deviation of, 10,10,10,10,10,10,16,16\displaystyle 10, 10, 10, 10, 10, 10, 16, 16 is
MCQ
3156
If X\displaystyle X and Y\displaystyle Y are related by 2X+3Y=4\displaystyle 2X+3Y=4 and SD of X\displaystyle X is 6, then SD of Y\displaystyle Y is
MCQ
3157
The standard deviation of 25,32,43,53,62,59,48,31,24,33\displaystyle 25, 32, 43, 53, 62, 59, 48, 31, 24, 33 is
MCQ
3158
The SD is independent of change of
MCQ
3159
If x\displaystyle x and y\displaystyle y are related by y=2x+5\displaystyle y = 2x + 5 and the SD and AM of x\displaystyle x are known to be 5\displaystyle 5 and 10\displaystyle 10 respectively, then the coefficient of variation of y\displaystyle y is
MCQ
3160
If the SD of x\displaystyle x is 3\displaystyle 3, what us the variance of (5−x)\displaystyle (5-x)?
MCQ
3161
If the values of all observations are equal then the Standard Deviation of the given observations is
MCQ
3162
The Standard Deviation of a set of 50\displaystyle 50 items is 10\displaystyle 10. Find the Standard Deviation if every item is increased by 5\displaystyle 5
MCQ
3163
Find the coefficient of variation if the sum of squared deviations taken from mean 40\displaystyle 40 of 10\displaystyle 10 observations is 360\displaystyle 360.
MCQ
3164
If x\displaystyle x and y\displaystyle y are related by 2x+3y+4=0\displaystyle 2x+3y+4=0 and SD of x\displaystyle x is 9\displaystyle 9, then SD of y\displaystyle y is
MCQ
3165
What is the coefficient of variation of the following numbers 53,52,61,60,64\displaystyle 53, 52, 61, 60, 64
MCQ
3167
If X\displaystyle X and Y\displaystyle Y are two random variables then v(x+y)\displaystyle v(x+y), when x\displaystyle x is independent of y\displaystyle y
MCQ
3168
The sum of squares of deviation from mean of 10\displaystyle 10 observations is 250\displaystyle 250. Mean of the data is 10\displaystyle 10. Find the coefficient of variation
MCQ
3169
If variance of is x\displaystyle x is 5\displaystyle 5, then find the variance of (2−3x)\displaystyle (2-3x)
MCQ
3170
What is the standard deviation of number recoveries among 48\displaystyle 48 patients when the probability of recovering is 0.75\displaystyle 0.75?
MCQ
3171
The standard deviation of 10,16,10,16,10,10,16,16\displaystyle 10, 16, 10, 16, 10, 10, 16, 16 is
MCQ
3172
The variance of the data 3,4,5,8\displaystyle 3, 4, 5, 8 is
MCQ
3174
Which measure of dispersion is based on all the observations?
MCQ
3177
The of mean and SD of a series is a+b\displaystyle a+b, if we add 2 to each observation of the series then the sum of the mean and SD is
MCQ
3179
Standard deviation of first n\displaystyle n natural number is 2. What is the value of n\displaystyle n?
MCQ
3180
Find the variance of 3x+2\displaystyle 3x+2 if standard deviation of x\displaystyle x is 4
MCQ
3181
If the variance of x=148.6\displaystyle x = 148.6 and mean of x=40\displaystyle x = 40, then the coefficient of variation is
MCQ
3182
If x\displaystyle x and y\displaystyle y are related by y=2x+5\displaystyle y = 2x+5 and the SD and AM of x\displaystyle x are known to be 5 and 10 respectively., then the coefficient of variation of y\displaystyle y is
MCQ
3183
If x\displaystyle x and y\displaystyle y are related by y=2x+5\displaystyle y = 2x+5 and the SD and AM of x\displaystyle x are known to be 5 and 10 resp., then the coefficient of variation of y\displaystyle y is
MCQ
3184
SD of first five consecutive natural numbers is:
MCQ
3185
If the profit of a company remains same for the last 10 months then the SD of profit of the company would be:
MCQ
3186
The SD of a variable x\displaystyle x is to be 10. SD of 50+5x\displaystyle 50+5x is
MCQ
3187
If mean and coefficient of variation of the marks of n\displaystyle n students is 20 and 80 respectively. What will be variance of them
MCQ
3188
If the standard deviation of 1,2,3,4,...,10\displaystyle 1, 2, 3, 4, ..., 10 is σ\displaystyle \sigma, then the SD of 11,12,13,14,...,20\displaystyle 11, 12, 13, 14, ..., 20 is:
MCQ
3189
What is the SD of the following series : Meas. | 0-10 | 10-20 | 20-30 | 30-40 Freq. | 1 | 3 | 4 | 2
MCQ
3190
If all observations in a distribution are increased by 6, then the variance of the series will be ____
MCQ
3191
The arithmetic mean and coefficient of variation of data set x\displaystyle x are respectively 10 and 30. The variance of 30−2x\displaystyle 30-2x is
MCQ
3192
If 2x+3y=0\displaystyle 2x + 3y = 0 and v(x)=6\displaystyle v(x) = 6 then v(y)\displaystyle v(y) is:
MCQ
3193
If the profit of a company remain same for the last 10 months then the SD of profit would be:
MCQ
3194
The sum of mean and SD of a series is a+b\displaystyle a + b, if we add 2\displaystyle 2 to each observation of the series then the sum of mean and SD is:
MCQ
3195
If the coefficient of variation and standard deviation are 60\displaystyle 60 and 12\displaystyle 12 respectively, then the arithmetic mean of the distribution is
MCQ
3196
If the sum of square of the value equals to 3390\displaystyle 3390, Number of observation are 30\displaystyle 30 and Standard deviation is 7\displaystyle 7, what is the mean value of the above observation?
MCQ
3197
If the variance of random variable 'x\displaystyle x' is 18\displaystyle 18, then what is variance of y=2x+5\displaystyle y = 2x + 5?
MCQ
3199
There are two startups in ecommerce sector struggling to acquire the market. Following data is for Mean and Standard Deviation of billing amount of bought items per month on their website.Startup | A | BNo. of customers/Month | 40 | 30Mean billing amount | 2,500∣\displaystyle 2,500 |2,200SD of billing amount | 10∣\displaystyle 10 |11Which startup has a better consistency in terms of sales numbers?
MCQ
3200
Which of the following is the best measure to calculate the volatility of stock market?
MCQ
3201
If mean and coefficient of variation of the marks of 10\displaystyle 10 students is 20\displaystyle 20 and 80\displaystyle 80 respectively. What will be the variance of them?
MCQ
3202
If the same amount is added or subtracted from all the of the individual series then the standard deviation and variance both shall be ______.
MCQ
3205
If 5\displaystyle 5 is subtracted from each observation of some certain item then its co-efficient of variation is 10%\displaystyle 10\% and 5\displaystyle 5 is added to each item then its coefficient of variation is 8%\displaystyle 8\%. Find original coefficient of variation.
MCQ
3206
Suppose a population A has 100\displaystyle 100 observations 101,102,103,...,200\displaystyle 101, 102, 103, ..., 200 and another population B has 100\displaystyle 100 observations 151,152,153,...,250\displaystyle 151, 152, 153, ..., 250. If VA\displaystyle V_A and VB\displaystyle V_B represents the variance of the two populations respectively, then VA/VB\displaystyle V_A / V_B ______.
MCQ
3207
If variance of x\displaystyle x is 5\displaystyle 5, then find the variance of (2−3x)\displaystyle (2 - 3x)
MCQ
3209
If the Standard Deviation of 10\displaystyle 10 observations is 4\displaystyle 4 and if each item is divided by −2\displaystyle -2 then Standard Deviation of new series is
MCQ
3210
For a set of 100\displaystyle 100 observations, taking assumed mean as 4\displaystyle 4, the sum of the deviations is −11\displaystyle -11 cm, and the sum of the squares of these deviations is 257\displaystyle 257 cm2\displaystyle ^2. The coefficient of variation is:
MCQ
3211
Mean and S.D. of x\displaystyle x is 50\displaystyle 50 and 5\displaystyle 5 respectively. Find mean and S.D. of X=−50\displaystyle X = -50
MCQ
3212
If the mean of frequency distribution is 100\displaystyle 100 and coefficient of variation is 45%\displaystyle 45\% then SD is
MCQ
3213
If the mean and SD of X\displaystyle X are a\displaystyle a and b\displaystyle b respectively, then the S.D of X−a\displaystyle X - a is
MCQ
3214
If the same amount is added or subtracted from all the of an individual series then the standard deviation and variance both shall be
MCQ
3215
If all the observations are increased by 6\displaystyle 6, then the variance of the series will be
MCQ
3216
(Q3−Q1)\displaystyle (Q_3 - Q_1) is known as
MCQ
3222
The approximate ratio SD, MD, QD is:
MCQ
3223
If the first quartile in 56.50\displaystyle 56.50 and the third quartile is 77.50\displaystyle 77.50, then the co-efficient of QD is:
MCQ
3224
_________ is based on all the observations and _________ is based on the central fifty percent of the observations.
MCQ
3225
Which one of the following is not a method of measures of dispersion?
MCQ
3226
For a given set of normally distributed data, the following statistical parameters are known: Mean =6\displaystyle = 6, Standard deviation =2.6\displaystyle = 2.6, Median =5\displaystyle = 5 and Quartile deviation =1.5\displaystyle = 1.5, then the coefficient of quartile deviation equals to
MCQ
3227
If the first quartile is 42.75\displaystyle 42.75 and the third quartile is 74.25\displaystyle 74.25, then the coefficient of QD is:
MCQ
3228
If the quartile deviation is 12\displaystyle 12 and the first quartile is 25\displaystyle 25, then the value of the third quartile is:
MCQ
3229
If 'x' and 'y' are related as 3x−4y=20\displaystyle 3x - 4y = 20 and the quartile deviation of 'x' is 12\displaystyle 12, then the quartile deviation of 'y' is:
MCQ
3230
If in a data set, 25\displaystyle 25 percent of values are smaller than 30\displaystyle 30 and one-fourth of values are larger than 70\displaystyle 70, then the coefficient of quartile deviation is _________ %
MCQ
3231
In which of the following there is no impact of presence of extreme observations?
MCQ
3233
The quartiles of a variable are 45,52\displaystyle 45, 52 and 65\displaystyle 65 respectively. Its quartile deviation is
MCQ
3234
Quartiles can be determined graphically using a
MCQ
3235
Which measures of dispersions is not affected by the presence of extreme observations?
MCQ
3236
Which measure is based on only the central fifty percent of the observations?
MCQ
3237
The appropriate measure of dispersion for open-end classification is
MCQ
3238
The quartiles of a variable are 45\displaystyle 45, 52\displaystyle 52 and 75\displaystyle 75 respectively. Its quartile deviation is
MCQ
3239
If x\displaystyle x and y\displaystyle y are related as 3x+4y=20\displaystyle 3x + 4y = 20 and the quartile deviation of x\displaystyle x is 16\displaystyle 16, then the QD of y\displaystyle y is
MCQ
3240
The quartiles of the variables are 45\displaystyle 45, 52\displaystyle 52, and 65\displaystyle 65 respectively, Its Quartile Deviation is
MCQ
3241
Interval Quartile Range is ______ of QD
MCQ
3242
In the equation 4x+2y=3\displaystyle 4x + 2y = 3, quartile deviation for y\displaystyle y is 3\displaystyle 3. Find the quartile deviation for x\displaystyle x.
MCQ
3243
If the quartile deviation of x\displaystyle x is 6\displaystyle 6 and 3x+6y=20\displaystyle 3x + 6y = 20, what is the quartile deviation of y\displaystyle y?
MCQ
3245
If x\displaystyle x and y\displaystyle y are related as 3x−4y=20\displaystyle 3x - 4y = 20 then the Quartile Deviation of x\displaystyle x is 12\displaystyle 12, then the Quartile deviation of y\displaystyle y is:
MCQ
3246
The QD from the following observations is 10,18,20,28,15,17,22,25,29,32,34\displaystyle 10, 18, 20, 28, 15, 17, 22, 25, 29, 32, 34 is equal to:
MCQ
3247
The QD of six numbers 13,8,36,40,38,41\displaystyle 13, 8, 36, 40, 38, 41 is equal to:
MCQ
3248
Coefficient of Quartile Deviation is 1/4\displaystyle 1/4 then QD is?
MCQ
3249
If the SD of a variable X\displaystyle X is σ\displaystyle \sigma then Quartile Deviation (QD) is
MCQ
3250
Which one is an absolute measure of dispersion?
MCQ
3251
A shift of origin has no impact on
MCQ
3252
Which measure is based on all the observations
MCQ
3253
Which of the below is affected by shifting of scale
MCQ
3254
The Quartile deviation is
MCQ
3255
The approximate ratio of SD: MD: QD is
MCQ
3256
______ is based on all the observations and ______ is based on the central fifty percent of the observations.
MCQ
3257
If the first quartile is 56\displaystyle 56, and the third quartile is 77\displaystyle 77, then the co-efficient of quartile deviation is
MCQ
3261
If X\displaystyle X and Y\displaystyle Y are related as 3X−4Y=20\displaystyle 3X - 4Y = 20 and the quartile deviation of X\displaystyle X is 12\displaystyle 12, then the quartile deviation of Y\displaystyle Y is:
MCQ
3262
For a moderately skewed distribution, quartile deviation and the standard deviation are related by:
MCQ
3263
If the first quartile is 142\displaystyle 142 and semi-inter quartile range is 18\displaystyle 18, then the value of median is
MCQ

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