Question

For a data consisting of $15$ observations $x_i , i = 1, 2 , 3 ,...., 15$ the following results are obtained: $\sum^{15}_{i =1} x_i = 170 ; \sum^{15}_{i = 1} x_1^2 = 2830 $ .If one of the observation namely $20$ was found wrong and was replaced by its collect value $30$. then the corrected variance is

• A. 80
• B. 78
• C. 76
• D. 75

Answer 1

Answer: (B)

Given,
$\Sigma x^{2}=2830$ and $ \Sigma x=170$
Increase in $\Sigma x=10$
and increase in $\Sigma x^{2}=(30)^{2}-(20)^{2}$
$=900-400=500 $
$\Sigma x'=170+10=180$
and $\Sigma x'^{ 2}=2830+500=3330$
We know that, variance $=\frac{\Sigma x^{2}}{n}-\left(\frac{\Sigma x}{n}\right)^{2}$
$= \frac{3330}{15}-\left(\frac{180}{15}\right)^{2}$ [here, $ n=15$]
$= 222-144=78$