Question

Average height and variance of $5$ students in a class is $150$ and $18$ respectively. If we add one student whose height is $156cm$ then new variance is

• A. $21$
• B. $24$
• C. $25$
• D. $20$

Answer 1

The correct option is D $20$

Variance

${\sigma }^2=\left(\frac{\sum x{i}^2}{n}\right)-(\frac{\sum xi}{n}{)}^2$

Mean$\overline{x}=\frac{\sum xi}{5}=150$

$\overline{x}=\frac{\sum xi}{5}=150$

$\sum xi=750$

$\frac{\sum xi}{5}-(\overline{x}{)}^2=18$

or

$\frac{\sum x{i}^2}{5}-(150{)}^2=18$ $\sum x{i}^2=112590$

Let $\times 6=156$

$\overline{xn}={\sum }_{i+1}^6\times \frac{i}{6}=\frac{750+156}{6}=151.$

New variance

${\sum }_{121}^6\frac{x{i}^2}{6}-(\overline{xn}{)}^2=\frac{112590+(156{)}^2}{6}-({156}^2)$

=20