Q. 313.7( 3 Votes )

Let a, b, c, d, e

Answer :

Given observations are a, b, c, d, e

So the mean of the 5 observations is



∑xi=a+b+c+d+e=5m……..(i)


And the standard deviation of the 5 observations is



Substituting equation (i) in above equation we get




Now we will find the mean and standard deviation of the observations a + k, b + k, c + k, d + k, e + k, we get


So the mean of these 5 observations is




Substituting value from equation (i), we get



m1=m+k…………(iii)


And the standard deviation of the 5 observations is




Substituting equation (iii) in above equation we get





Substituting the value from equation (i), we get




Cancelling like terms, we get



Comparing this with equation (ii), we get


σ=s


Hence the standard deviation of new set of observations, i.e., a + k, b + k, c + k, d + k, e + k is s, itself.

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