Let v_1 be the variance of {13, 16, 19, dots, | vedclass

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(D) The variance of a set of numbers ${a, a+d, a+2d, \dots, a+nd}$ is equal to the variance of ${0, d, 2d, \dots, nd}$,which is $d^2 	imes 	ext{Var}

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$1 : 4$

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(D) The variance of a set of numbers ${a, a+d, a+2d, \dots, a+nd}$ is equal to the variance of ${0, d, 2d, \dots, nd}$,which is $d^2 	imes 	ext{Var}(\{0, 1, 2, \dots, n\})$.For the first set $S_1 = \{13, 16, 19, \dots, 103\}$,the common difference is $d_1 = 3$. The set can be written as $13 + 3k$ for $k = 0, 1, \dots, 30$. Thus,$v_1 = 3^2 	imes 	ext{Var}(\{0, 1, 2, \dots, 30\}) = 9 	imes 	ext{Var}(\{0, 1, 2, \dots, 30\})$.For the second set $S_2 = \{20, 26, 32, \dots, 200\}$,the common difference is $d_2 = 6$. The set can be written as $20 + 6k$ for $k = 0, 1, \dots, 30$. Thus,$v_2 = 6^2 	imes 	ext{Var}(\{0, 1, 2, \dots, 30\}) = 36 	imes 	ext{Var}(\{0, 1, 2, \dots, 30\})$.Therefore,the ratio is $\frac{v_1}{v_2} = \frac{9}{36} = \frac{1}{4}$.

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
$f_i$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

Let $v_1$ be the variance of $\{13, 16, 19, \dots, 103\}$ and $v_2$ be the variance of $\{20, 26, 32, \dots, 200\}$. Then the ratio $v_1 : v_2$ is:

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