Question

An incomplete distribution is given as follows:

Variable:	0−10	10−20	20−30	30−40	40−50	50 − 60	60 − 70
Frequency:	10	20	?	40	?	25	15

You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Answer 1

Let the frequency of the class 20−30 be and that of class 40−50 be. The total frequency is 170. So,

So, .....(1)

It is given that median is 35 which lies in the class 30-40. So 30-40 is the median class.

Now, lower limit of median class

Height of the class

Frequency of median class

Cumulative frequency of preceding median class

Total frequency

Formula to be used to calculate median,

Where,

- Lower limit of median class

- Height of the class

- Frequency of median class

- Cumulative frequency of preceding median class

- Total frequency

Put the values in the above,

Using equation (1), we have

Therefore,