Let a, b, c, d and e be the observations with mean m and standard deviation S . The standard deviation of the observations a+k , b+k, c+k, d+k and e+k is

Step-by-step solution

The given observation are a, b, c, d and e Mean =m= a+b+c+d+e 5 x_i=a+b+c+d+e=5 m ....(i) Now, consider the observations a+k, b+k, c+k , d+k, e+k . Now, mean = (a+k)+(b+k)+(c+k)+(d+k)+(e+k) 5 = a+b+c+d+e+5 k 5 = 5 m+5 k 5 =m+k New standard devaition = (x_i+k )^2 5 -(m+k)^2 = (x_i^2+k^2+2 x_i k ) 5 - (m^2+k^2+2 m k ) = x_i^2 5 -m^2+ 5 k^2 5 -k^2+ 2 k x_i 5 -2 m k = x_i^2 5 -m^2+ 2 k 5 m 5 -2 m k = x_i^2 5 -m^2 =S