Question

The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively. Later on, three observations, $3,4$ and $5$, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is.

• A. $8.00$
• B. $8.50$
• C. $8.25$
• D. $9.00$

Answer 1

The correct option is D $9.00$

$\sum _{i=1}^{97}{x}_i=400-(3+4+5)$
$=388$
$\sum _{i=1}^{97}{x}_i^2=2475-(9+16+25)$
$=2425$
Variance $=\frac{{\sum }_i{x}_i^2}{N}-{\left(\frac{\sum x_i}{N}\right)}^2$
$=\frac{2425}{97}-{\left(\frac{388}{97}\right)}^2$
$=25-4^2$
$=25-16=9$.