Question

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

• A. 188.66
• B. 177.33
• C. 8.33
• D. 78

Answer 1

Answer: (D)

78

Incorrect $\sum x^2=2830,n=15,\sum x=170+(30-20)=180$
Correct $\sum x^2=2830+(30{)}^2-(20{)}^2=2830+500=3330$
$\therefore$ Correct variance is ${\sigma }^2=\frac{\text{Corrected}(\sum x^2)}{n}-{\left(\frac{\text{Corrected}\sum x^2}{n}\right)}^2$
$\Rightarrow {\sigma }^2=\frac{3330}{15}-{\left(\frac{180}{15}\right)}^2=222-144=78$