The variance of the observations $2,3,5,7,11$, $13,17,22$ is

The variance of the observations $2,3,5,7,11$, $13,17,22$ is
  1. 43.75
  2. 48.25
  3. 80
  4. 350

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

Asked in: AP EAMCET 2019 (20 Apr Shift 2)

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