The variance of the following data is: x_i | vedclass

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(C) To calculate the variance,we use the assumed mean method where $a = 18$. The calculations are as follows:   $x_i$ $f_i$ $d_i = x_i - 18$ $f_i d_i$

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$43.4$

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(C) To calculate the variance,we use the assumed mean method where $a = 18$. The calculations are as follows:   $x_i$ $f_i$ $d_i = x_i - 18$ $f_i d_i$ $f_i d_i^2$   $6$ $2$ $-12$ $-24$ $288$   $10$ $4$ $-8$ $-32$ $256$   $14$ $7$ $-4$ $-28$ $112$   $18$ $12$ $0$ $0$ $0$   $24$ $8$ $6$ $48$ $288$   $28$ $4$ $10$ $40$ $400$   $30$ $3$ $12$ $36$ $432$   Total $N = 40$ - $\sum f_i d_i = 40$ $\sum f_i d_i^2 = 1776$   The formula for variance is $\sigma^2 = \frac{\sum f_i d_i^2}{N} - \left(\frac{\sum f_i d_i}{N}\right)^2$. Substituting the values: $\sigma^2 = \frac{1776}{40} - \left(\frac{40}{40}\right)^2$ $\sigma^2 = 44.4 - (1)^2$ $\sigma^2 = 44.4 - 1 = 43.4$.

The variance of the following data is:

$x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$

$f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

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The variance of the following data is: $x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$ $f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$