Q75 / 160 · AP EAMCET 2019 (20 Apr Shift 2) · Mathematics
The variance of the observations $2,3,5,7,11$, $13,17,22$ is
- Correct answerA43.75
- B48.25
- C80
- D350
Solution
According to the given information,
$$ \begin{aligned} \bar{x} & =\frac{\sum x_i}{8}=\frac{80}{8}=10 \\ \because \quad \sum\left(x_i-\bar{x}\right)^2 & =350 \end{aligned} $$ $\therefore$ Variance of the given observations $=\frac{\Sigma\left(x_i-\bar{x}\right)^2}{8}$ $$ =\frac{350}{8}=43.75 $$ Hence, option (a) is correct.
$$ \begin{aligned} \bar{x} & =\frac{\sum x_i}{8}=\frac{80}{8}=10 \\ \because \quad \sum\left(x_i-\bar{x}\right)^2 & =350 \end{aligned} $$ $\therefore$ Variance of the given observations $=\frac{\Sigma\left(x_i-\bar{x}\right)^2}{8}$ $$ =\frac{350}{8}=43.75 $$ Hence, option (a) is correct.
Hence, the correct answer is option: 'A'.