An incomplete distribution is given as follows:

It is given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula fill up the missing frequency.

To find: The median I.Q.

Formula Used:

Median = l + × h

l = lower limit of median class

f = frequency of median class

h = size of the median class

F = cumulative frequency preceding the median class.

Explanation:

Given, Median = 35

The median class = 30-40

l = 30, h = 10, f = 40 and F = 30 + f₁

Median = l +

f₁ = 55 – 20 = 35

Given, Sum of frequencies = 170

= 10 + 20 + f₁ + 40 + f₂ + 25 + 15 = 170

= 10 + 20 + 35 + 40 + f₂ + 25 + 15 = 170

= f₂ = 170 – 145 = 25

Therefore, f₁ = 35 and f₂ = 25