The variance of the observations 2, 3, 5, 7, | vedclass

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(A) The given observations are $x_i = \{2, 3, 5, 7, 11, 13, 17, 22\}$.First,calculate the mean $(\bar{x})$:$\bar{x} = \frac{\sum x_i}{n} = \frac{2+3+5

Vedclass · Accepted Answer

$43.75$

Vedclass · Answer

(A) The given observations are $x_i = \{2, 3, 5, 7, 11, 13, 17, 22\}$.First,calculate the mean $(\bar{x})$:$\bar{x} = \frac{\sum x_i}{n} = \frac{2+3+5+7+11+13+17+22}{8} = \frac{80}{8} = 10$.Next,calculate the sum of squared deviations $\sum (x_i - \bar{x})^2$:$(2-10)^2 + (3-10)^2 + (5-10)^2 + (7-10)^2 + (11-10)^2 + (13-10)^2 + (17-10)^2 + (22-10)^2$$= (-8)^2 + (-7)^2 + (-5)^2 + (-3)^2 + (1)^2 + (3)^2 + (7)^2 + (12)^2$$= 64 + 49 + 25 + 9 + 1 + 9 + 49 + 144 = 350$.The variance is given by $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n} = \frac{350}{8} = 43.75$.Thus,the correct option is $A$.

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

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