Question

In an experiment with $15$ observations on $x$, the following results were available $\Sigma x^{2}=2830, \Sigma x=170$ One 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)

Given $N=15$
$\Sigma x^{2}=2830, \Sigma x=170$
One observation 20 was replaced by $30,$ then
$\Sigma x^2 = 2830 - 400 + 900 = 3330$
$\Sigma x = 170 - 20 + 30 = 180$
Varience, $\sigma^2 = \frac{\Sigma x^2}{N} - \left(\frac{\Sigma x}{N}\right)^2$
$ = \frac{3330}{15} - \left(\frac{180}{15}\right)^2$
$= \frac{3330 - 15 \times 144}{15}$
$ = \frac{3330 - 2160}{15} = \frac{1170}{15} = 78.0$