The variance of the observations 8, 12, 13, 1 | vedclass

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Question

(B) The given observations are $8, 12, 13, 15, 22$. Here,the number of observations $n = 5$. The mean $\overline{x} = \frac{8 + 12 + 13 + 15 + 22}{5}

Vedclass · Accepted Answer

$21.2$

Vedclass · Answer

(B) The given observations are $8, 12, 13, 15, 22$. Here,the number of observations $n = 5$. The mean $\overline{x} = \frac{8 + 12 + 13 + 15 + 22}{5} = \frac{70}{5} = 14$. The variance is given by the formula $\sigma^2 = \frac{\sum (x_i - \overline{x})^2}{n}$. Calculating the squared deviations from the mean: $(8 - 14)^2 = (-6)^2 = 36$ $(12 - 14)^2 = (-2)^2 = 4$ $(13 - 14)^2 = (-1)^2 = 1$ $(15 - 14)^2 = (1)^2 = 1$ $(22 - 14)^2 = (8)^2 = 64$ Sum of squared deviations $= 36 + 4 + 1 + 1 + 64 = 106$. Variance $= \frac{106}{5} = 21.2$.

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$11$	$29$	$18$	$4$	$5$	$3$

The variance of the observations $8, 12, 13, 15, 22$ is:

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