Question

The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 –30 and the number of observations less than 20 is 45, then the frequency of median class is ______.

Options

• 10

• 20

• 15

• 12

Answer 1

The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 –30 and the number of observations less than 20 is 45, then the frequency of median class is 10.

Explanation:

Median is given as

M = `l + (N/2 - F)/f xx C`

where

l = lower limit of the median class

f = frequency of the median class

N = total frequency

F = cumulative frequency of the class just before the median class

C = length of median class

Now, given, M = 25, N = 100, F = 45,

C = 20 – 30 = 10, l = 20.

∴ By using the formula, we have

25 = `20 + (50 - 45)/f xx 10`

⇒ f = 10