Question

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

• A. $78$
• B. $188.6666$
• C. $177.3333$
• D. $8.3333$

Answer 1

The correct option is A $78$

Given that $\sum x^2=2830$ , $\sum x=170$

Given that one observation $20$ was replaced by $30$

Therefore, $\sum x=170-20+30=180$ and

$\sum x^2=2830-(20{)}^2+(30{)}^2=3330$

Given that, number of observations $n=15$

Variance is given by $\frac{\sum x^2}{n}-(\frac{\sum x}{n}{)}^2$

$=\frac{3330}{15}-(\frac{180}{15}{)}^2=\frac{3330-15\ast 144}{15}$

$=\frac{1170}{15}=78$