Q. 124.6( 46 Votes )

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

[Hint Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval]

Answer :

We first convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval and then form the following table adding the other columns after calculations.

The class interval containing or 50^{th} item is 35.5-40.5. Therefore, 35.5-40.5 is the median class.

Now, we know that

Median

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

Therefore, Median

So, we can calculate the absolute values of the deviations from the median, i.e., |x_{i} – Med.|, as shown in the table.

Therefore, we have

And

Hence, the mean deviation about the median for the given data is 7.35.

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