In an experiment with 15 observations on x, the following results were available: x^2=2830…

Question

In an experiment with 15 observations on x, the following results were available: $\sum x^2=2830$, $\sum x=170$. One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is

Accepted Answer

Corrected sum: $\sum x' = 170+(30-20)=180$
Corrected sum of squares: $\sum x'^2 = 2830+(900-400)=3330$

$$\text{Variance} = \frac{3330}{15}-\left(\frac{180}{15}\right)^2 = 222-144=78$$

Solutions · 1