Question

In an experiment with 15 observations on $x$, the 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 $30$. 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

$\sum x=170,\sum x^2=2830$
Increase in $\sum x=30-20=10$, then
$\sum x^{\prime }=170+10=180$
Increase in $\sum x^2={30}^2-{20}^2=900-400=500$ then
$\sum x^{\prime 2}=2830+500=3330$
Variance $=\frac{1}{n}\sum x^{\prime 2}-{(\frac{1}{n}\sum x^{\prime })}^2$
$=\frac{1}{15}\times 3330-{(\frac{1}{15}\times 180)}^2=222-144=78$