Find the variance of the following data: 6, 8 | vedclass

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(A) The given data is $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$. The number of observations $n = 10$.First,calculate the mean $\bar{x}$:$\bar{x} = \frac{

Vedclass · Accepted Answer

$33$

Vedclass · Answer

(A) The given data is $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$. The number of observations $n = 10$.First,calculate the mean $\bar{x}$:$\bar{x} = \frac{6+8+10+12+14+16+18+20+22+24}{10} = \frac{150}{10} = 15$.Now,calculate the variance $\sigma^2$ using the formula $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$.The squared deviations $(x_i - \bar{x})^2$ are:$(6-15)^2 = (-9)^2 = 81$$(8-15)^2 = (-7)^2 = 49$$(10-15)^2 = (-5)^2 = 25$$(12-15)^2 = (-3)^2 = 9$$(14-15)^2 = (-1)^2 = 1$$(16-15)^2 = (1)^2 = 1$$(18-15)^2 = (3)^2 = 9$$(20-15)^2 = (5)^2 = 25$$(22-15)^2 = (7)^2 = 49$$(24-15)^2 = (9)^2 = 81$Sum of squared deviations = $81+49+25+9+1+1+9+25+49+81 = 330$.Variance $\sigma^2 = \frac{330}{10} = 33$.

Find the variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$

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