If the median of the following frequency distribution is 28.5 find the missing frequencies: Class interval: 0 - 10, 10 - 20, 30 - 40

Question

If the median of the following frequency distribution is 28.5 find the missing frequencies:

Answer 1

Given: 

The frequency table. 

To find: 

The missing frequencies f₁ and f₂ . 

Solution: 

Construct a table to calculate cumulative frequencies,The table is shown below:

As it lies in the interval 20-30, 

So, 

median class is 20-30 

Now, l, lower class = 20, frequency of median class, f = 20, Cumulative frequency of class preceding the median class, F = 5 + f₁, height of class, h = 10N is 60, 

we know,

f₁ = 25 – 17 

f₁ = 8

Given, 

sum of frequencies = 60 

i.e. 5 + f₁ + 20 + 15 + f² + 5 = 60Put the value of f1 

therefore, 5 + 8 + 20 + 15 + f₂ + 5 = 60 

hence, 

f₂ = 7 

Therefore, 

f₁ = 8 and f₂ = 7