The variance of the data 2, 3, 5, 11, 13, 17, | vedclass

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(D) Given data: $2, 3, 5, 11, 13, 17, 19$,where $n = 7$. First,calculate the mean $(\bar{x})$: $\bar{x} = \frac{2 + 3 + 5 + 11 + 13 + 17 + 19}{7} = \f

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$39.71$

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(D) Given data: $2, 3, 5, 11, 13, 17, 19$,where $n = 7$. First,calculate the mean $(\bar{x})$: $\bar{x} = \frac{2 + 3 + 5 + 11 + 13 + 17 + 19}{7} = \frac{70}{7} = 10$. We know the formula for variance $(\sigma^2)$: $\sigma^2 = \frac{\sum_{i=1}^n x_i^2}{n} - (\bar{x})^2$. Calculate the sum of squares of the data: $\sum x_i^2 = 2^2 + 3^2 + 5^2 + 11^2 + 13^2 + 17^2 + 19^2 = 4 + 9 + 25 + 121 + 169 + 289 + 361 = 978$. Now,substitute the values into the variance formula: $\sigma^2 = \frac{978}{7} - (10)^2 = 139.714 - 100 = 39.714$. Thus,the variance is nearly $39.71$.

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

The variance of the data $2, 3, 5, 11, 13, 17, 19$ is nearly

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