Measures of Central Tendency and Dispersion

If the variables $\displaystyle x$ and $\displaystyle z$ are so related that $\displaystyle z = ax + b$ for each where $\displaystyle a$ and $\displaystyle b$ are constant, then $\displaystyle \bar{z} = a\bar{x} + b$.

If the mean of the following distribution is $\displaystyle 6$, then the value of $\displaystyle P$ is: \displaystyle \begin{array}{|c|c|c|c|c|c|} \hlineX\displaystyle & 2 & 4 & 6 & 10 &P+5\displaystyle \\ \hlineF\displaystyle & 3 & 2 & 3 & 1 & 2 \\ \hline \end{array}

There are $\displaystyle n$ numbers. When 50 is subtracted from each of these number the sum of the numbers so obtained is $\displaystyle -10$. When 46 is subtracted from each of the original $\displaystyle n$ numbers, then the sum of numbers so obtained is 70. What is the mean of the original $\displaystyle n$ numbers?

Which measure is suitable for open-end classification?

$\displaystyle 50^{th}$ Percentile is equal to

Find the median of the following. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Freq: 2, 3, 4, 5, 6

If each item is reduced by 15 A. M is

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.

The mean of 20 items of a data is 5 & if each item is multiplied by 3, then the new mean will be

The algebraic sum of the deviation of a set of values from their arithmetic mean is

Which one of the following is not a central tendency?

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

The AM of 15 observation is 9 and the AM of first 9 observation is 11 and then AM of remaining observation is

$\displaystyle \sum (x_i - \bar{x})$ is equal to

The mean of '$\displaystyle n$' observation is '$\displaystyle x$'. If $\displaystyle k$ is added to each observation, then the new mean is.

If there are 3 observations 15, 20, 25 then sum of deviation of the observations from AM is

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?

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

When each value does not have equal importance then we use

The mean of 20 observation is 38. If two observation are taken as 84 and 36 instead of 48 and 63 find new means.

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:

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?

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?

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

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:

If mean of 5 observations $\displaystyle x+1, x+3, x+5, x+7$ and $\displaystyle x+9$ is given 15, then the value of $\displaystyle x$ will be:

The mean of the first three terms is 17 and mean of next four terms is 21. Calculate the mean of seven terms.

If there are two groups containing 40 and 30 observations and have arithmetic means as 50 and 60, then the combined arithmetic mean is

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:

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

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:

If the relationship between two variables $\displaystyle u$ and $\displaystyle v$ are given by $\displaystyle 2u + 7v = 0$ and if the AM of $\displaystyle u$ is 10, then the AM of $\displaystyle v$ is

If there are 3 observations 15, 20, 25 then the sum of deviation of the observations from their AM is

The mean of the values of $\displaystyle 1, 2, 3, \dots, n$ with respective frequencies $\displaystyle x, 2x, 3x, \dots, nx$ is.

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

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?

The mean of first 3 terms is 14 and the mean of next 2 terms is 18. The mean of 5 numbers is

If the mean of the set of observations $\displaystyle x_1, x_2, x_3, \dots, x_n$ is $\displaystyle \bar{x}$, then the mean of the observation $\displaystyle x_i + ki$, where $\displaystyle i = 1, 2, 3, \dots, n$

The average of $\displaystyle n$ numbers is $\displaystyle x$. If each of the numbers is multiplied by $\displaystyle (n+1)$, then the average of new set of numbers is

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?

Two variables assume the values $\displaystyle 1, 2, \dots, 5$ with frequencies as $\displaystyle 1, 2, 3, \dots, 5$ then what is the AM?

The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their:

Let the mean of the variable '$\displaystyle x$' be 50, then the mean of $\displaystyle u=10+5x$ will be.

If sum of squares of the values = 3390, N = 30 and standard deviation = 7, find out the mean.

Which of the following measures of central tendency cannot be calculated by graphical method?

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?

The mean of the variable $\displaystyle x$ is 50, then the mean of $\displaystyle u=10+5x$ will be

The sum of mean and SD of a series is $\displaystyle a+b$, if we add 2 to each observations of the series then the sum of the mean and SD is

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.

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

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:

Mean of 25,32,43,53,62,59,48,31,24,33 is

If the A.M of any distribution be 25 & one term is 18. Then the deviation of 18 from A.M is

The algebraic sum of the deviations of a frequency distribution from its mean is always,

Pooled Mean is also called

If average marks for a group of $\displaystyle 30$ girls is $\displaystyle 80$, a group of boys is $\displaystyle 70$ and combined average is $\displaystyle 76$, then how many boys are in the group ?

If there are three observations $\displaystyle 15, 20, 25$, then the sum of deviation of the observations from their AM is.

The mean weight of $\displaystyle 15$ students is $\displaystyle 110$ kg. The mean weight of $\displaystyle 5$ of them is $\displaystyle 100$ kg, and of another five students is $\displaystyle 125$ kg, then the mean weight of the remaining students is :

A batsman in his $\displaystyle 20^{th}$ innings makes a score of $\displaystyle 120$ and thereby increases his average by $\displaystyle 5$. What is his average after $\displaystyle 20^{th}$ innings?

The mean of first three terms is $\displaystyle 14$ and mean of next two terms is $\displaystyle 18$. The mean of all five terms is

In a group of persons, average weight is $\displaystyle 60$ kg. If the average of males and females taken separately is $\displaystyle 80$ kg and $\displaystyle 50$ kg respectively, find the ratio of the number of males to that of females.

The mean of $\displaystyle 100$ students was $\displaystyle 45$. Later, it was discovered that the marks of two students were misread as $\displaystyle 85$ and $\displaystyle 54$ instead of $\displaystyle 58$ and $\displaystyle 45$. Find correct mean.

The AM of $\displaystyle 15$ observations is $\displaystyle 9$ and the AM of first $\displaystyle 9$ observations is $\displaystyle 11$ and then AM of remaining observations is:

The mean of $\displaystyle 100$ observations is $\displaystyle 50$. If one of the observations which was $\displaystyle 50$ is replaced by $\displaystyle 40$, the resulting mean will be:

The mean annual salary of all employees in a company is $\displaystyle 25,000$. The mean salary of male and female employees is $\displaystyle 27,000$ and $\displaystyle 17,000$ respectively. Find the percentage of males and females employed by the company.

The average age of $\displaystyle 15$ numbers in a class is $\displaystyle 9$ years. Out of them, the average age of $\displaystyle 5$ students is $\displaystyle 13$ years and that of $\displaystyle 8$ students is $\displaystyle 5$ years. What is the average of remaining $\displaystyle 2$ students?

The students of a class $\displaystyle 10^{th}$ have an average weight of $\displaystyle 50$ kg. The strength of the class is $\displaystyle 49$ students. On including the weight of the principal, the average weight shoots up by $\displaystyle 0.8$ kg. Find the weight of the principal?

The average of '$\displaystyle r$' consecutive numbers starting from $\displaystyle 1$ is '$\displaystyle r$'. If $\displaystyle 2$ is added to each of the number. Then the new average will be?

The average weight of $\displaystyle 40$ people is increased by $\displaystyle 2.4$ kg when one man weight $\displaystyle 73$ kg is replaced by another man. Find the weight of the new man?

The average salary of the whole employees in a company is $\displaystyle 400$ per day. The average salary of officers is $\displaystyle 800$ per day and that of clerks is $\displaystyle 320$ per day. If the number of officers is $\displaystyle 40$, then find the number of clerks in the company?

The average of $\displaystyle 6$ numbers is $\displaystyle 30$. If the average of the first four is $\displaystyle 25$ and that of the last three is $\displaystyle 35$, the fourth number is

A student marks were wrongly entered as $\displaystyle 85$ instead of $\displaystyle 45$. Due to that the average marks for the whole class got increased by one-fourth. The no. of students in the class is?

Find the median of the following. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Freq: 5, 8, 15, 10, 2

The mean salary of a group of $\displaystyle 50$ persons is Rs. $\displaystyle 5850$. Later on it is discovered that the salary of one has been wrongly taken as Rs. $\displaystyle 8000$ instead of Rs. $\displaystyle 7500$. The corrected mean salary is

The algebraic sum of the deviations of set of values from their arithmetic mean is

The AM of $\displaystyle 15$ observations is $\displaystyle 9$ and the AM of first $\displaystyle 9$ observations is $\displaystyle 11$ and then AM of remaining observations is

The weighted mean of first $\displaystyle n$ natural numbers, if their weights are proportional to their corresponding numbers is

The average wages of a group of unexperienced labours is $\displaystyle 1000$ and that of a group of experienced labours is $\displaystyle 1,500$. If the combined wage is $\displaystyle 1200$, then what is the percentage of experienced labours?

If the arithmetic mean of $\displaystyle 1^{st}$ $\displaystyle n$ natural numbers is $\displaystyle \frac{6n}{11}$ then the value of '$\displaystyle n$' is:

The average age of a group of $\displaystyle 10$ students was $\displaystyle 20$ 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 ?

There were $\displaystyle 50$ students in a class. $\displaystyle 10$ failed whose average marks were $\displaystyle 2.5$. The total marks of class were $\displaystyle 281$. Find the average marks of students who passed?

When $\displaystyle 10$ is subtracted from all the observations, the mean is reduced to $\displaystyle 60\%$ of its value. If $\displaystyle 5$ is added to all the observations, then the mean will be

The mean salary for a group of $\displaystyle 40$ female workers is $\displaystyle 5200$ per month and that for a group of $\displaystyle 60$ male workers is $\displaystyle 6800$ per month. What is the combined salary ?

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:

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 ____.

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?

The mean of the values of $\displaystyle 1, 2, 3, \dots, n$ with respective frequencies $\displaystyle x, 2x, 3x, \dots, nx$ is

Two variables $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 5x + 2y + 5 = 0$ and $\displaystyle x = 10$. If $\displaystyle y$ is

The mean of first 3 terms is 14 and the mean of next 2 terms is 18. The mean of 5 numbers is -

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:

The mean salary of a group of 50 persons is $\displaystyle ₹5850$. Later on it is discovered that the salary of one has been wrongly taken as $\displaystyle ₹8000$ instead of $\displaystyle ₹7800$. The corrected mean salary is:

The algebraic sum of the deviations of set of values from their arithmetic mean is:

The AM of 15 observations is 9 and the AM of first 9 observations is 11 and then AM of remaining observations is

Which one of these is least affected by extreme value?

Ten matches data is given. Then which of the following cannot be found?

Which of the following measure does not possess mathematical properties?

The median value of the set of observations $\displaystyle 48, 36, 72, 87, 19, 66, 56, 91$ is

Along a road there are 5 buildings of apartments, marked as $\displaystyle 1, 2, 3, 4, 5$. 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.

The $\displaystyle 3^{rd}$ decile for the numbers $\displaystyle 15, 10, 20, 25, 18, 11, 9, 12$ is

The relationship between two variables $\displaystyle x$ and $\displaystyle y$ is given by $\displaystyle 4x - 10y = 20$. If the median value of the variable $\displaystyle x$ is 10 then what is median value of variable $\displaystyle y$?

For $\displaystyle 899, 999, 391, 384, 390, 480, 485, 760, 111, 240$. Rank of median

The median of the data $\displaystyle 5, 6, 7, 8, 9, 10, 11, 12, 15, 18$, and $\displaystyle 19$ is

Which of the following is positional average?

For the distribution, The value of median is x: 1, 2, 3, 4, 5, 6; f: 6, 9, 10, 14, 12, 8

The deviations are minimum taken from:

Mean deviation is minimum when deviations are taken from:

The median of the observations $\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 56$ is:

The median of the following set of observation: $\displaystyle 24, 18, 36, 42, 30, 28, 21, 29, 25, 33$ is

For a given data set: $\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4$, what is the median?

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

If two variable '$\displaystyle x$' and '$\displaystyle y$' are related as $\displaystyle 2x - y = 3$. If the median of '$\displaystyle x$' is $\displaystyle 10$, what is median of '$\displaystyle y$'?

Which of the following measure of central tendency will be unaffected if the lowest and highest observation are removed?

Which of the following measure of central tendency depends on the position of the observation?

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

For open-end classification, which of the following is the best measure of central tendency?

The presence of extreme observations does not affect

Quartiles are the values dividing a given set of observations into

What is the value of the first quartile for observations $\displaystyle 15, 18, 10, 20, 23, 28, 12, 16$?

The third decile for the numbers $\displaystyle 15, 10, 20, 25, 18, 11, 9, 12$ is

Two variables $\displaystyle x$ and $\displaystyle y$ are given by $\displaystyle y = 2x - 3$. If the median of $\displaystyle x$ is $\displaystyle 20$, what is the median of $\displaystyle y$?

In case of an even number of observations which of the following is median?

Quartile can be determined graphically using

The point of intersection of less than ogive and greater than ogive curve is gives us

The median of data $\displaystyle 13, 8, 11, 6, 4, 15, 2, 18$ is

Find $\displaystyle D_6$ for the following observations. $\displaystyle 7, 9, 5, 4, 10, 15, 14, 18, 6, 20$

The median of $\displaystyle 27, 30, 26, 44, 42, 51, 37$ is

The median value of the set of observations $\displaystyle 48, 36, 72, 87, 19, 66, 56$ and $\displaystyle 91$

The first Quartile is $\displaystyle 142$ and Semi-inter Quartile Range is $\displaystyle 18$, then the value of Median is:

Calculate the value of 3rd quartile from the following data $\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 32$

For the distribution, calculate MedianX | 1 | 2 | 3 | 4 | 5 | 6F | 6 | 9 | 10 | 14 | 12 | 8

The relationship between two variable $\displaystyle x$ and $\displaystyle y$ is given by $\displaystyle 4x - 10y = 20$. If the median value of the variable $\displaystyle x$ is $\displaystyle 20$ then what is median value of variable $\displaystyle y$?

The median of the observations $\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 56$ is

The median of following numbers, which are given in ascending order is $\displaystyle x, 25, 30, 35, 39, 46, x+1, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46$.

The third decile for the numbers $\displaystyle 35, 10, 20, 25, 18, 11, 12$ and $\displaystyle 12$ is

If the relationship between $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 4x - 6y = 13$ & median of $\displaystyle x$ is $\displaystyle 16$. Find median of $\displaystyle y$.

Find $\displaystyle Q_1$ for the following observations: $\displaystyle 7,9,5,4,10,15,14,18,6,20$

The wages of $\displaystyle 8$ workers expressed in rupees are $\displaystyle 42,45,49,38,56,54,55,47$. Find median wage?

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

Histogram is used to represent

Find the mode of the following:0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-607 | 14 | 22 | 34 | 20 | 19

From the record on sizes of shoes sold in a shop, one can compute the following to determine the most preferred shoe size.

If $\displaystyle y = 3 + (4.5)x$ and the mode for $\displaystyle x$ - value is $\displaystyle 20$, then the mode for $\displaystyle y$ - value is

If $\displaystyle y = 3 + 1.9x$, and mode of $\displaystyle x$ is $\displaystyle 15$, then the mode of $\displaystyle y$ is:

Mean Deviation of data $\displaystyle 3, 10, 10, 4, 7, 18, 5$ from mode is

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

The Geometric mean of $\displaystyle 3, 6, 24$ and $\displaystyle 48$ is

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?

If two variables $\displaystyle a$ and $\displaystyle b$ are related by $\displaystyle c = ab$ then G.M. of $\displaystyle c$ is equal to

Given the weights for the numbers $\displaystyle 1, 2, 3, \dots, n$ are respectively $\displaystyle 1^2, 2^2, 3^2, \dots, n^2$ then weighted HM is

The harmonic mean $\displaystyle A$ and $\displaystyle B$ is $\displaystyle 1/3$ and harmonic mean of $\displaystyle C$ and $\displaystyle D$ is $\displaystyle 1/5$. The harmonic mean of $\displaystyle ABCD$ is

A fire engine rushes to a place of fire accident with a speed of $\displaystyle 110$ kmph and after the completion of operation returned to the base at a speed of $\displaystyle 55$ kmph. The average speed per hour in per-direction is obtained as ________ speeds.

If there are two groups with $\displaystyle n_1$ and $\displaystyle n_2$ observations and $\displaystyle H_1$ and $\displaystyle H_2$ are respective harmonic means, then the harmonic mean of combined observation is

Find the mode of the following data:X | F(x)25-30 | 2030-35 | 5335-40 | 4240-45 | 4245-50 | 4150-55 | 43

Geometric Mean of $\displaystyle 3, 7, 11, 15, 24, 28, 30, 0$ is

If the arithmetic mean of two numbers is $\displaystyle 10$ and the geometric mean is $\displaystyle 6$, then the difference in the numbers is

If two variables $\displaystyle a$ and $\displaystyle b$ are related by $\displaystyle c = ab$ then GM. of $\displaystyle c$ =

Geometric Mean of $\displaystyle 8, 4, 2$ is

The geometric mean of the numbers $\displaystyle 40, 50$, and $\displaystyle x$ is $\displaystyle 10$, and the value of $\displaystyle x$ is

A man travels from Delhi to Agra at an average speed of $\displaystyle 30 \text{km per hour}$ and back at an average speed of $\displaystyle 60 \text{km per hour}$. What's the average speed.

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle x - y - 10 = 0$ and mode of $\displaystyle x$ is known to be $\displaystyle 23$, then the mode of $\displaystyle y$ is

A person travels from A to B at the rate of $\displaystyle 20 \text{ km/hr}$ and from B to A at the rate of $\displaystyle 30 \text{ km/hr}$. What is the average rate of whole journey?

If there are two groups with $\displaystyle 75$ and $\displaystyle 65$ as harmonic means containing $\displaystyle 15$ and $\displaystyle 13$ observation, then combined HM is given by

The Geometric mean of the series $\displaystyle 1, k, k^2, k^3, ..., k^n$ where $\displaystyle k$ is constant is

A man travels at a speed of $\displaystyle 20 \text{km/hr}$ and then returns at a speed of $\displaystyle 30 \text{km/hr}$. His average speed of the whole journey is:

G.M is a better measure than others when,

If there are two groups with $\displaystyle 75$ and $\displaystyle 65$ as harmonic means and containing $\displaystyle 15$ and $\displaystyle 13$ observations. Then the combined H.M. is given by:

If there are two groups with $\displaystyle 75$ and $\displaystyle 65$ as harmonic means and containing $\displaystyle 15$ and $\displaystyle 13$ observations, then the combined HM is given by

A train covered the first $\displaystyle 5 \text{ km}$ of its journey at a speed of $\displaystyle 30 \text{km/hr}$, and the next $\displaystyle 15 \text{ km}$ at a speed of $\displaystyle 45 \text{ km/hr}$. The average speed of the train was:

Mode is:

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?

The Harmonic mean H of two numbers is $\displaystyle 4$ and their arithmetic means $\displaystyle A$ and the geometric mean $\displaystyle G$ satisfy eq. $\displaystyle 2A + G^2 = 27$, the numbers are

The harmonic mean of $\displaystyle 1, 1/2, 1/3, ..., 1/n$ is

The rate of returns from three different shares are $\displaystyle 100\%, 200\%$ and $\displaystyle 400\%$ respectively. The average rate of return will be.

Relation between mean, median and mode is

If in a moderately skewed distribution, the values of mode and mean are $\displaystyle 32.1$ and $\displaystyle 35.4$ respectively, then the value of the median is

In a moderately skewed distribution the values of mean & median are $\displaystyle 12$ & $\displaystyle 8$ respectively. The value of mode is

For a symmetric distribution

If the AM & GM of two numbers are $\displaystyle 30$ and $\displaystyle 24$ respectively. Find the no's.

If the AM and HM of two numbers are $\displaystyle 6$ and $\displaystyle 9$ respectively, then GM is

If the AM and GM for 10 observations are both 15, then the value of HM is

For a moderately skewed distribution, the median is twice the mean, then mode is _times the median.

Given that mean = 70.20 and mode = 70.50, the Median is expected to be.

If Mean ($\displaystyle X$) is = 10 and mode ($\displaystyle Z$) is = 7, then find out the value of median ($\displaystyle M$).

If Arithmetic Mean and Geometric Mean between two numbers are 5 and 4 respectively, then these two numbers are:

If Arithmetic mean between two numbers is 5 and Geometric mean is 4 then what is the value of Harmonic mean?

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?

If the mean of two numbers is 30 and geometric mean is 24, then what will be the Harmonic mean of two numbers?

The AM and HM of two numbers are 5 and 3.2 respectively, then GM will be:

If mode of a grouped data is 10 and median is 6, then what is the value of mean?

If A.M and G.M of two positive numbers $\displaystyle a$ and $\displaystyle b$ are 12 and 12, respectively, find the numbers

If the mean and median of a moderately asymmetrical series are 26.8 and 27.9 respectively, then the most probable mode is:

If Mean of a data set is 22 and Median is 22.33 then Mode is

According to the empirical rule, if the data form a "bell-shaped" distribution, then the maximum and minimum frequencies occur at ______ and ______ respectively.

If the mean and median of a moderately asymmetrical series are 70.8 and 68.6 respectively, then the most probable mode is:

For a moderately-skewed distribution, which of the following relationship holds?

If the arithmetic mean between two numbers is 64 and the Geometric Mean between them is 16. The Harmonic mean between them is ______.

When the mean is 3.57 and mode is 2.13, then the value of median is ______.

The relationship between AM, GM, and Median

Relationship between AM, GM, and HM

For a moderately skewed distribution, which is true

Which of the following results hold for a set of distinct positive observations?

For a moderately skewed distribution, which of the following relationship holds?

If the A.M. and H.M. for two numbers are 5 and 3.2 respectively then the G.M. will be:

Which of the following statements is true?

When mean is 3.57 and mode is 2.13 then the value of the median is

The A.M and H.M for two numbers are 5 and 3.2 respectively then the G.M will be

Which of the following is not a criteria for ideal measure of central tendency?

If the rates return from three different shares are $\displaystyle 100\%$, $\displaystyle 200\%$ and $\displaystyle 400\%$ respectively. The average rate of return will be.

Find the two numbers if AM and GM is $\displaystyle 10$ and $\displaystyle 6$ respectively.

For moderately skewed distribution, the median is twice the mean, then mode is \_ times the median.

Which of the following is the correct relation between mean, median and mode

If the mode of a data is $\displaystyle 18$ and mean is $\displaystyle 24$, then median is

For a moderately skewed distribution, which of the following relationship is correct

The mode of data is $\displaystyle 18$ and mean is $\displaystyle 24$, then median is

Find the numbers whose GM is $\displaystyle 5$ and AM is $\displaystyle 7.5$:

If the difference between mean and mode is $\displaystyle 69$, then the difference between Mean and Median will be _______.

Which of the following result hold for a set of distinct positive observations?

______ & ______ are called ratio averages:

The Arithmetic Mean between two numbers is $\displaystyle 15$ and their G.M. is $\displaystyle 9$; then the numbers are $\displaystyle -$

If the arithmetic mean between two numbers is $\displaystyle 64$ and the Geometric Mean between them is $\displaystyle 16$. The Harmonic mean between them is

When the mean is $\displaystyle 3.57$ and mode is $\displaystyle 2.13$, then the value of median is _______.

The HM, $\displaystyle H$ of two numbers is $\displaystyle 4$ and their AM, $\displaystyle A$ and the GM, $\displaystyle G$ satisfy the equation $\displaystyle 2A+G^2=27$, the numbers are:

If the range of a set of values is $\displaystyle 65$ and maximum value in the set is $\displaystyle 83$, then the minimum value in the set is

Difference between upper limit and lower limit of a class is known as.

The relationship between P-series and Q-series is given by $\displaystyle 2P - 3Q - 10 = 0$. If the range of P-series is $\displaystyle 18$. What would be the range of Q?

If the relationship between $\displaystyle x$ and $\displaystyle y$ is given by $\displaystyle 2x + 3y = 10$ and the range of $\displaystyle y$ is $\displaystyle 10$, then what is the range of $\displaystyle x$?

The marks secured by $\displaystyle 5$ students in a subject are $\displaystyle 82, 73, 69, 84, 66$. What is the coefficient of Range?

If the range of data is $\displaystyle 20$ and its smallest value is $\displaystyle 5$, then what is the largest value of data is?

What is the coefficient of range for the observations $\displaystyle 20, 28, 32, 41, 48, 50$?

What is the range of a data set?

If the range of $\displaystyle x$ is $\displaystyle 2$, find range of $\displaystyle -3x + 50$?

The range of the $\displaystyle 15, 12, 10, 9, 17, 20$ is

The range of $\displaystyle 15, 12, 10, 9, 17, 30$ is

If $\displaystyle R_x$ and $\displaystyle R_y$ denote ranges of $\displaystyle x$ and $\displaystyle y$ respectively where $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 3x+2y+10=0$, what would be the relation between $\displaystyle x$ and $\displaystyle y$?

If the range of $\displaystyle 28, 22, 40, 20, 15, 50$ is

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

Which of the following is a correct statement?

If $\displaystyle R_x$ and $\displaystyle R_y$ denote ranges of $\displaystyle x$ and $\displaystyle y$ respectively where $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 4x+5y+12=0$, what would be the relation between $\displaystyle R_x$ and $\displaystyle R_y$?

________ is an absolute measure of dispersion.

Which of the following measure of dispersion is based on absolute deviations?

Find the coefficient of mean deviation for mean for the data: $\displaystyle 5, 7, 8, 10, 11, 13, 19$

If a school has $\displaystyle 14$ teachers, their heights (in cm) are: $\displaystyle 172, 173, 164, 178, 168, 169, 173, 172, 173, 164, 178, 168, 169, 173$ then average deviation of this data is:

The probable value of mean deviation when $\displaystyle Q_3 = 40$ and $\displaystyle Q_1 = 15$ is:

If every observation is increased by $\displaystyle 7$ then:

The mean deviation of the numbers $\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 12$ about the mean is:

Which of the below is based on absolute deviation?

If $\displaystyle x$ and $\displaystyle y$ are related as $\displaystyle 4x+3y+11=0$ and mean deviation of $\displaystyle y$ is $\displaystyle 7.20$, what is the mean deviation of $\displaystyle x$?

The mean deviation about the mean for the data $\displaystyle 12, 16, 24, 30, 35, 39, 40$ is

If Mean deviation of Arithmetic Mean is $\displaystyle 1.78$ and Arithmetic Mean is $\displaystyle 3.50$ then coefficient of Mean deviation about Arithmetic mean is

The MD about the Mean for the data $\displaystyle 6,9,11,10,12$ is

The mean deviation about Mode for the numbers $\displaystyle 4/11, 6/11, 8/11, 9/11, 12/11, 8/11$ is

If the relation between $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 5y - 3x = 10$ and the mean deviation about mean for $\displaystyle x$ is $\displaystyle 12$, then the mean deviation of $\displaystyle y$ about mean is

If two variables $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 2x + 3y = 0$ and the mean and mean deviation about mean of $\displaystyle x$ are $\displaystyle 1$ and $\displaystyle 0.3$ respectively, then the co-efficient of mean deviation of $\displaystyle y$ about mean is:

The equation of a line is $\displaystyle 5x + 2y = 17$. Mean deviation of $\displaystyle y$ about mean is $\displaystyle 5$. Calculate mean deviation of $\displaystyle x$ about mean.

The deviations are minimum when taken from

The sum of squares of the deviations of the given values from their ................. is minimum.

Which measure of dispersion is based on the absolute deviation only?

Find the mean deviation about mean for the numbers: $\displaystyle 2, 6, 7, 4, 8, 3$

If the relation between $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 4y - 3x = 10$ and the mean deviation about mean for $\displaystyle x$ is $\displaystyle 12$, then the mean deviation of $\displaystyle y$ about mean is

If two variables $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 2x + 3y - 7 = 0$ and the mean and mean deviation about mean of $\displaystyle X$ are $\displaystyle 1$ and $\displaystyle 0.3$ respectively, then the co-efficient of mean deviation of $\displaystyle Y$ about mean is.

The relation between two variables is $\displaystyle 2x - 3y + 12 = 0$ If mean deviation of $\displaystyle y$ is $\displaystyle 6$ then mean deviation of $\displaystyle x$ is

If two variables $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 2x$ and $\displaystyle 3y - 7 = 0$ and the mean and mean deviation about mean of $\displaystyle x$ are $\displaystyle 1$ and $\displaystyle 0.3$ respectively, then the coefficient of mean deviation of $\displaystyle y$ about mean is:

If the S.D. of the $\displaystyle 1^{st}$ $\displaystyle n$ natural numbers is $\displaystyle \sqrt{30}$ then the value of $\displaystyle n$ is

If the variance of $\displaystyle 5, 7, 9$ and $\displaystyle 11$ is $\displaystyle 4$, then the coefficient of variation is:

Standard Deviation for the marks obtained by a student in monthly test in mathematic (out of $\displaystyle 50$) as $\displaystyle 30, 35, 25, 20, 15$ is

If the standard deviation for the marks obtained by a student in monthly test is $\displaystyle 36$, then variance is

If $\displaystyle \sigma^2 = 100$ & coefficient of variation $\displaystyle = 20\%$ then $\displaystyle x$

S.D of first five consecutive natural numbers is

If the profits of a company remain some for the last ten months then the S.D. of profits of the company would be:

The sum of mean and SD of a series is $\displaystyle a + b$, if we add $\displaystyle 2$ to each observation of the series then the sum of mean and SD is

Origin is shifted by $\displaystyle 5$, what will happen

Coefficient of variation is equal to:

Find SD of the following $\displaystyle 1, 2, 3, 4, 5, 6, 7, 8, 9.$

If mean $\displaystyle = 200$ and variance $\displaystyle = 80$. Find coefficient of variation.

Which of the below is affected by shifting of scale.

Coefficient of variation is $\displaystyle 80$. Mean is $\displaystyle 20$. Find variance:

SD from numbers $\displaystyle 1, 4, 5, 7, 8$ is $\displaystyle 2.45$. If $\displaystyle 10$ is added to each then SD will be:

The best statistical measure used for comparing two series is

It is given that the mean ($\displaystyle X$) 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:

The SD of 1 to 9 natural number is:

If the numbers are $\displaystyle 5, 1, 8, 7, 2$ then the coefficient of variation is:

AM and Coefficient of variation of $\displaystyle x$ is 10 and 40. What is the variance $\displaystyle 30-2x$?

Following are the wages of 8 workers $\displaystyle 82, 96, 52, 75, 70, 65, 50, 70$. Find range and coefficient of range?

Find the standard deviation and coefficient of variation for $\displaystyle 1, 9, 8, 7, 5$.

If the coefficient of variation and standard deviation are 30 and 12 respectively, then the arithmetic mean of the distribution is:

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?

If the variance of random variable '$\displaystyle x$' is 17, then what is variance of $\displaystyle y = 2x+5$?

If the variance of given data is 12, and their mean value is 40, what is coefficient of variation (CV)?

In a given set if all data are of same value then variance would be:

If the Standard Deviation of data $\displaystyle 2, 4, 5, 6, 8, 17$ is $\displaystyle 4.47$, then Standard Deviation of the data $\displaystyle 4, 8, 10, 12, 16, 34$ is

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?

For the first 20 natural numbers the standard deviation is ________.

If Arithmetic mean and Coefficient of variations of $\displaystyle x$ are 5 and 20 respectively, the variance of $\displaystyle 12-3x$ is

Consider the data sets: $\displaystyle X = [-6, 2, -2, 6]$, $\displaystyle Y = [4, 8, 2, 6]$ $\displaystyle Z = [103, 100, 102, 101]$ Let $\displaystyle S_X, S_Y, S_Z$ be the standard deviations of the sets $\displaystyle X, Y$ and $\displaystyle Z$ respectively. We have the relations,

If each observation of a set is divided by 10, then the Standard Deviation of the new observation is:

The Standard Deviation of the series is $\displaystyle 3, 6, 9, 12, 15$ is:

If the mean of frequency distribution is 100 and coefficient of variation is $\displaystyle 45\%$, then Standard deviation is

If the mean and SD of $\displaystyle X$ are $\displaystyle a$ and $\displaystyle b$ respectively, then the S.D of $\displaystyle X = \frac{X-a}{b}$ is

Coefficient of Variation (CV) is calculated

The SD for the data $\displaystyle 6, 9, 10, 3, 7$ is

The standard deviation of, $\displaystyle 10, 10, 10, 10, 10, 10, 16, 16$ is

If all the observations are multiplied by 2, then

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?

If $\displaystyle X$ and $\displaystyle Y$ are related by $\displaystyle 2X+3Y=4$ and SD of $\displaystyle X$ is 6, then SD of $\displaystyle Y$ is

The standard deviation of $\displaystyle 25, 32, 43, 53, 62, 59, 48, 31, 24, 33$ is

The SD is independent of change of

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle y = 2x + 5$ and the SD and AM of $\displaystyle x$ are known to be $\displaystyle 5$ and $\displaystyle 10$ respectively, then the coefficient of variation of $\displaystyle y$ is

If the SD of $\displaystyle x$ is $\displaystyle 3$, what us the variance of $\displaystyle (5-x)$?

If the values of all observations are equal then the Standard Deviation of the given observations is

The Standard Deviation of a set of $\displaystyle 50$ items is $\displaystyle 10$. Find the Standard Deviation if every item is increased by $\displaystyle 5$

Find the coefficient of variation if the sum of squared deviations taken from mean $\displaystyle 40$ of $\displaystyle 10$ observations is $\displaystyle 360$.

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 2x+3y+4=0$ and SD of $\displaystyle x$ is $\displaystyle 9$, then SD of $\displaystyle y$ is

What is the coefficient of variation of the following numbers $\displaystyle 53, 52, 61, 60, 64$

The mean and SD for $\displaystyle a, b,$ and $\displaystyle 2$ are $\displaystyle 3$ and $\displaystyle 1$ respectively, the value of $\displaystyle ab$ would be

If $\displaystyle X$ and $\displaystyle Y$ are two random variables then $\displaystyle v(x+y)$, when $\displaystyle x$ is independent of $\displaystyle y$

The sum of squares of deviation from mean of $\displaystyle 10$ observations is $\displaystyle 250$. Mean of the data is $\displaystyle 10$. Find the coefficient of variation

If variance of is $\displaystyle x$ is $\displaystyle 5$, then find the variance of $\displaystyle (2-3x)$

What is the standard deviation of number recoveries among $\displaystyle 48$ patients when the probability of recovering is $\displaystyle 0.75$?

The standard deviation of $\displaystyle 10, 16, 10, 16, 10, 10, 16, 16$ is

The variance of the data $\displaystyle 3, 4, 5, 8$ is

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 ?

Which measure of dispersion is based on all the observations?

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.

The Standard Deviation of a variable $\displaystyle x$ is known to be 10. The Standard deviation of $\displaystyle 50+5x$

The of mean and SD of a series is $\displaystyle a+b$, if we add 2 to each observation of the series then the sum of the mean and SD is

If all the observations are decreased by 4, find the relation between new SD and old SD.

Standard deviation of first $\displaystyle n$ natural number is 2. What is the value of $\displaystyle n$?

Find the variance of $\displaystyle 3x+2$ if standard deviation of $\displaystyle x$ is 4

If the variance of $\displaystyle x = 148.6$ and mean of $\displaystyle x = 40$, then the coefficient of variation is

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle y = 2x+5$ and the SD and AM of $\displaystyle x$ are known to be 5 and 10 respectively., then the coefficient of variation of $\displaystyle y$ is

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle y = 2x+5$ and the SD and AM of $\displaystyle x$ are known to be 5 and 10 resp., then the coefficient of variation of $\displaystyle y$ is

SD of first five consecutive natural numbers is:

If the profit of a company remains same for the last 10 months then the SD of profit of the company would be:

The SD of a variable $\displaystyle x$ is to be 10. SD of $\displaystyle 50+5x$ is

If mean and coefficient of variation of the marks of $\displaystyle n$ students is 20 and 80 respectively. What will be variance of them

If the standard deviation of $\displaystyle 1, 2, 3, 4, ..., 10$ is $\displaystyle \sigma$, then the SD of $\displaystyle 11, 12, 13, 14, ..., 20$ is:

What is the SD of the following series : Meas. | 0-10 | 10-20 | 20-30 | 30-40 Freq. | 1 | 3 | 4 | 2

If all observations in a distribution are increased by 6, then the variance of the series will be ____

The arithmetic mean and coefficient of variation of data set $\displaystyle x$ are respectively 10 and 30. The variance of $\displaystyle 30-2x$ is

If $\displaystyle 2x + 3y = 0$ and $\displaystyle v(x) = 6$ then $\displaystyle v(y)$ is:

If the profit of a company remain same for the last 10 months then the SD of profit would be:

The sum of mean and SD of a series is $\displaystyle a + b$, if we add $\displaystyle 2$ to each observation of the series then the sum of mean and SD is:

If the coefficient of variation and standard deviation are $\displaystyle 60$ and $\displaystyle 12$ respectively, then the arithmetic mean of the distribution is

If the sum of square of the value equals to $\displaystyle 3390$, Number of observation are $\displaystyle 30$ and Standard deviation is $\displaystyle 7$, what is the mean value of the above observation?

If the variance of random variable '$\displaystyle x$' is $\displaystyle 18$, then what is variance of $\displaystyle y = 2x + 5$?

If the variance of given data is $\displaystyle 12$, and their mean value is $\displaystyle 40$, what is coefficient of variation (CV)?

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 | $\displaystyle 2,500 |$2,200SD of billing amount | $\displaystyle 10 |$11Which startup has a better consistency in terms of sales numbers?

Which of the following is the best measure to calculate the volatility of stock market?

If mean and coefficient of variation of the marks of $\displaystyle 10$ students is $\displaystyle 20$ and $\displaystyle 80$ respectively. What will be the variance of them?

If the same amount is added or subtracted from all the of the individual series then the standard deviation and variance both shall be ______.

If the S.D. of $\displaystyle x$ is $\displaystyle 4$, what is the variance of $\displaystyle (5 - 2x)$?

Mean and S.D. of a given set of observations is $\displaystyle 1,500$ and $\displaystyle 400$ respectively. If there is an increment of $\displaystyle 100$ in the first year and each observation is hiked by $\displaystyle 20\%$ in $\displaystyle 2$nd years, then find new mean and S.D.

If $\displaystyle 5$ is subtracted from each observation of some certain item then its co-efficient of variation is $\displaystyle 10\%$ and $\displaystyle 5$ is added to each item then its coefficient of variation is $\displaystyle 8\%$. Find original coefficient of variation.

Suppose a population A has $\displaystyle 100$ observations $\displaystyle 101, 102, 103, ..., 200$ and another population B has $\displaystyle 100$ observations $\displaystyle 151, 152, 153, ..., 250$. If $\displaystyle V_A$ and $\displaystyle V_B$ represents the variance of the two populations respectively, then $\displaystyle V_A / V_B$ ______.

If variance of $\displaystyle x$ is $\displaystyle 5$, then find the variance of $\displaystyle (2 - 3x)$

The sum of the squares of deviations of a set of observations has the smallest value, when the deviations are taken from their

If the Standard Deviation of $\displaystyle 10$ observations is $\displaystyle 4$ and if each item is divided by $\displaystyle -2$ then Standard Deviation of new series is

For a set of $\displaystyle 100$ observations, taking assumed mean as $\displaystyle 4$, the sum of the deviations is $\displaystyle -11$ cm, and the sum of the squares of these deviations is $\displaystyle 257$ cm$\displaystyle ^2$. The coefficient of variation is:

Mean and S.D. of $\displaystyle x$ is $\displaystyle 50$ and $\displaystyle 5$ respectively. Find mean and S.D. of $\displaystyle X = -50$