Q

# Calculate the mean deviation about median age for the age distribution of 100 persons given below: (12)

12.    Calculate the mean deviation about median age for the age distribution of persons given below:

 Age (in years) Number

[Hint  Convert the given data into continuous frequency distribution by subtracting from the lower limit and adding to the upper limit of each class interval]

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 Age (in years) Number Cumulative Frequency c.f. Mid Points 15.5-20.5 5 5 18 20 100 20.5-25.5 6 11 23 15 90 25.5-30.5 12 23 28 10 120 30.5-35.5 14 37 33 5 70 35.5-40.5 26 63 38 0 0 40.5-45.5 12 75 43 5 60 45.5-50.5 16 91 48 10 160 50.5-55.5 9 100 53 15 135 =735

Now, N = 100, which is even.

The class interval containing  or  item is 35.5-40.5. Therefore, 35.5-40.5 is the median class.

We know,

Median

Here, l = 35.5, C = 37, f = 26, h = 5 and N = 100

Therefore, Median

Now, we calculate the absolute values of the deviations from median,   and

= 735

Hence, the mean deviation about the median is 7.35

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