Q. 3
Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number.
Answer :
Given: set of first n natural numbers when n is an odd number
To find: the mean deviation about the mean
We know first n natural numbers are 1, 2, 3….., n. And given n is odd number.
So mean is,
The deviations of numbers from the mean are as shown below,
Or,
Or,
So the absolute values of deviation from the mean is
The sum of absolute values of deviations from the mean, is
i.e., 2 times sum of terms, so it can be written as
Therefore, mean deviation about the mean is
Hence the mean deviation about the mean of the set of first n natural numbers when n is an odd number is
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Calculate the mean deviation about the mean of the set of first n natural numbers when n is an even number.
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