Question

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

• A. 78.00
• B. 188.66
• C. 177.33
• D. 8.33

Answer 1

Answer: (A)

78.00

Answer 2

$\sum x = 170$, $\sum x^{2} = 2830$

Increase in $\sum x = 10$, then $\sum x^{'} = 170 + 10 = 180$

Increase in $\sum x^{2} = 900 - 400 = 500$, then

$\sum x^{'2} = 2830 + 500 = 3330$

∴ Variance $= \frac{1}{n}\sum x^{'2} - \left( \frac{\sum x^{'}}{n} \right)^{2}$

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