If mean and standard deviation of 5 observations x_1,x_2,x_3,x_4,x_5 are 10 and 3, respect…

Question

If mean and standard deviation of 5 observations $x_1,x_2,x_3,x_4,x_5$ are 10 and 3, respectively, then the variance of 6 observations $x_1,x_2,\ldots,x_5$ and $-50$ is equal to:

Accepted Answer

$\sum_{i=1}^5 x_i = 50$; $\dfrac{\sum x_i^2}{5}-100=9 \implies \sum x_i^2=545$

Including $-50$: $\sum_{i=1}^6 x_i = 50-50=0$; $\sum_{i=1}^6 x_i^2 = 545+2500=3045$

$$\text{Variance} = \frac{3045}{6}-0^2 = 507.5$$

Solutions · 1