Central Tendency & DispersionPYQ Nov. 19Question 2954 of 473
All Questions

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

Options

A35
B32
C36
D37.5
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 32

All Options:

  • A35
  • B32
  • C36
  • D37.5

Detailed Solution & Explanation

We are given the grouped frequency distribution: - Class Interval: 0−10,10−20,20−30,30−40,40−50\displaystyle 0-10, 10-20, 20-30, 30-40, 40-50 - Frequency (f\displaystyle f): 2,3,4,5,6\displaystyle 2, 3, 4, 5, 6 1. Compute cumulative frequencies (cf\displaystyle cf): - 0−10\displaystyle 0-10: cf=2\displaystyle cf = 2 - 10−20\displaystyle 10-20: cf=2+3=5\displaystyle cf = 2 + 3 = 5 - 20−30\displaystyle 20-30: cf=5+4=9\displaystyle cf = 5 + 4 = 9 - 30−40\displaystyle 30-40: cf=9+5=14\displaystyle cf = 9 + 5 = 14 - 40−50\displaystyle 40-50: cf=14+6=20\displaystyle cf = 14 + 6 = 20 2. Total frequency N=20\displaystyle N = 20, so N2=10\displaystyle \frac{N}{2} = 10. 3. The cumulative frequency just greater than 10\displaystyle 10 is 14\displaystyle 14, which corresponds to the median class 30−40\displaystyle 30-40. Thus: - Lower limit of median class: L=30\displaystyle L = 30 - Cumulative frequency of preceding class: cf=9\displaystyle cf = 9 - Frequency of median class: f=5\displaystyle f = 5 - Class interval width: i=10\displaystyle i = 10 4. Applying the median formula: Median=L+N2−cff×i=30+10−95×10=30+15×10=32\text{Median} = L + \frac{\frac{N}{2} - cf}{f} \times i = 30 + \frac{10 - 9}{5} \times 10 = 30 + \frac{1}{5} \times 10 = 32 Hence, **Option B** is the correct answer.

More Questions from Central Tendency & Dispersion

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

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

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:

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

If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are

Which of the following is not a method of dispersion?

Ready to Master Central Tendency & Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free