The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively.

Question

The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is?

Accepted Answer

Mean $=9 \implies \sum x_i=45$. S.D.$=0 \implies$ all five values are 9.

Changed observation: $\dfrac{36+x_5}{5}=10 \implies x_5=14$

$$\sigma_{new} = \sqrt{\frac{4(9-10)^2+(14-10)^2}{5}} = \sqrt{\frac{4+16}{5}}=\sqrt4=2$$

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