Q4 of 46 Page 278

Calculate the mean deviation about the mean of the set of first n natural numbers when n is an even number.

Given: set of first n natural numbers when n is an even number.


To find: the mean deviation about the mean


We know first n natural numbers are 1, 2, 3….., n. And given n is even 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




Now we know sum of first n natural numbers = n2


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 even number is


More from this chapter

All 46 →
2

Find the mean deviation about the median of the following distribution:

 3

Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number.

 5

Find the standard deviation of the first n natural numbers.

 6

The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results:

Number of observations = 25, mean = 18.2 seconds, standard deviation = 3.25 seconds.


Further, another set of 15 observations x1, x2, ..., x15, also in seconds, is now available and we have


and . Calculate the standard derivation based on all 40 observations.