Let a, b, c, d, e, be the observations with m and standard deviation s. The standard deviation of the observations a+k, b+k, c+k, d+k, e+k is `s` (b) `k s` (c) `s+k` (d) `s/k`

Explanation

Mean `=m=frac{a+b+c+d+e}{5}`

`Rightarrow sum x_{i}=a+b+c+d+e=5 m ldots .(i)` Standard deviation,`s=sqrt{frac{sum x_{i}^{2}}{5}-m^{2}}`

consider the observations `a+k, b+k, c+k, d+k, e+k`

New mean

`therefore` New standard deviation

`=sqrt{frac{sum(x_{i}+k)^{2}}{5}-(m+k)^{2}}`

`=sqrt{frac{sqrt{2(x_{i}^{2}+k^{2}+2 x_{i} k)}}{5}-(m^{2}+k^{2}+2 m k)}`

`sqrt{frac{sum x_{i}^{2}}{5}+frac{Sigma k^{2}}{5}+frac{Sigma 2 x_{i} k}{5}-(m^{2}+k^{2}+2 m k)}`

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