Question

An incomplete distribution is given below :

Variable:	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	12	30	−	65	−	25	18

You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.

Answer 1

(i) Let the missing frequencies be x and y.

First we prepare the following cummulative table.

Here,

So,

It is given that the median is 46.

Therefore, is the median class.

We know that

Also,

Putting the value of x, we get

Hence, the missing frequencies are 34 and 46.

(ii)

We may prepare the table as shown.

We know that mean,

Now, we have.

Putting the values in the above formula, we have

Hence, the mean is 45.87.