For a statistical data of 10 values, a student obtained the mean as 5.5 and _i=1^10x_i^2 =…

Question

For a statistical data of 10 values, a student obtained the mean as 5.5 and $\displaystyle\sum_{i=1}^{10}x_i^2 = 371$. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is:

Accepted Answer

$\sum x_i = 5.5\times10 = 55$

New sum: $55-(4+5)+(6+8) = 60$
New sum of squares: $371-(4^2+5^2)+(6^2+8^2) = 371-41+100 = 430$

$$\sigma^2 = \frac{430}{10} - \left(\frac{60}{10}\right)^2 = 43-36 = 7$$

Solutions · 1