Q) The monthly expenditure on milk in 200 families of a Housing Society is given below:

Find the value of x and also, find the median and mean expenditure on milk.

Ans:

(i) Value of x:

Let’s re-organize the data in the frequency table and calculate the value of x:

By summing up the families, we get:

24 + 40 + 33 + x + 30 + 22 + 16 + 7 = 200

  x = 200 -172 = 28

(ii) Median expenditure on milk:

To find the median, we need to identify middle value of the data. Let’s rearrange the data:

• First, we need to find the cumulative frequency in the frequency table to find the median. Its shown in last column.
• Next, Total number of families or sum of the frequencies = 200. It shown in the last row of middle column.
• Next, the Median class is the class where the cumulative frequency crosses 50% of the half the total number of families. Here in the table, Cumulative frequency of 125 is crossing 50% of frequencies i.e. 100, at class “2500-3000”. Hence, our Median class = 2500-3000
• Next, To find the median, we use the formula:

Median = L+x h

Here:

L = Lower boundary of the median class = 2500

n = Total number of families = 200

= Cumulative frequency of the class before the median class = 97

f = Frequency of the median class = 28

h = Class width = 3000 – 2500 = 500

hence, the Median = 2500 + x 500

⇒ 2500 + [(100 – 97)] x = 2500 + = 2553.57

Therefore, Median expenditure on the milk is Rs. 2,553.57

(iii) Mean expenditure on milk:

Let’s re-arrange the data with midpoint of each class, frequency, and multiply midpoint with frequency:

We know that, mean of grouped data is given by:

Mean of grouped data =

Therefore, Mean = = 2662.50

Hence, the mean expenditure om milk is Rs. 2,662.50