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 mean expenditure

Ans:

(i) Value of X:

To calculate the value of X, we first sum up all the frequencies:

Here, from 2nd column, we get total number of families = 172 + X

In the question, it is given that the total number of families = 200

∴ 172 + X = 200

∴ X = 200 – 172 = 28

Therefore, the value of X is 28.

(ii) Mean value of expenditure:

To find the mean value, we put X = 28 in the table and rearrange the data:

To re-arrange the above data, we take the following steps:

• We calculate midpoint ‘x’ of each class by
• Then we calculate ‘fx’ by multiplying midpoint of each class with frequency of that class
• We calculate Σf by summing up all the frequencies and Σfx by adding up all the values of fx

Next, we know that, mean of grouped data is given by:

Mean of grouped data =

Therefore, Mean value = = 2,662.50

Hence, the mean value of the given data is 2,662.50

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