Question

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

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

Answer 1

The correct option is B $78.00$

We know, Standard deviation, ${\sigma }^2=\frac{\sum x_i^2}{n}-{\left(\frac{\sum x}{n}\right)}^2$
$\therefore$ Corrected variance $=\frac{2830-{20}^2+{30}^2}{15}-{\left(\frac{170-20+30}{15}\right)}^2=222-144=78$