Mean of 5 observations is 7.

Question

Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is:

Accepted Answer

Missing observation: $\dfrac{6+7+8+10+x}{5}=7 \implies x=4$

$$\text{Variance} = \frac{(6-7)^2+(7-7)^2+(8-7)^2+(10-7)^2+(4-7)^2}{5} = \frac{1+0+1+9+9}{5}=\frac{20}{5}=4$$

*(Note: direct computation gives variance $=4$ (Option A). The source's final line instead takes $\sqrt4=2$ --- i.e. it reports the standard deviation, not the variance the question asks for --- yet records the answer as Option D (2). This appears to be an error in the original source rather than an extraction artifact.)*

Solutions · 1