Q5 of 46 Page 278

Find the standard deviation of the first n natural numbers.

Given: set of first n natural numbers


To find: the standard deviation


given first n natural numbers, we can write in table as shown below



So, the sums of these are




Therefore, the standard deviation can be written as,










Hence the standard deviation of the first n natural numbers is


More from this chapter

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3

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

 4

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

 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.

 7

The mean and standard deviation of a set of n1 observations are and s1, respectively while the mean and standard deviation of another set of n2 observations are and s2, respectively. Show that the standard deviation of the combined set of (n1 + n2) observations is given by