Find the variance of the following frequency | vedclass

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(D) Let $a = 7$ (assumed mean) and $h = 2$ (class width).      $Class$    $x_i$    $f_i$    $u_i = (x_i - a)/h$    $f_i u_i$    $f_i u_i^2$        $0-

Vedclass · Accepted Answer

$4.97$

Vedclass · Answer

(D) Let $a = 7$ (assumed mean) and $h = 2$ (class width).      $Class$    $x_i$    $f_i$    $u_i = (x_i - a)/h$    $f_i u_i$    $f_i u_i^2$        $0-2$    $1$    $2$    $-3$    $-6$    $18$        $2-4$    $3$    $7$    $-2$    $-14$    $28$        $4-6$    $5$    $12$    $-1$    $-12$    $12$        $6-8$    $7$    $19$    $0$    $0$    $0$        $8-10$    $9$    $9$    $1$    $9$    $9$        $10-12$    $11$    $1$    $2$    $2$    $4$        Total    -    $N=50$    -    $\sum f_i u_i = -21$    $\sum f_i u_i^2 = 71$  The formula for variance is $\sigma^2 = h^2 \left[ \frac{\sum f_i u_i^2}{N} - \left( \frac{\sum f_i u_i}{N} ight)^2 ight]$.Substituting the values:$\sigma^2 = 2^2 \left[ \frac{71}{50} - \left( \frac{-21}{50} ight)^2 ight]$$\sigma^2 = 4 \left[ 1.42 - (-0.42)^2 ight]$$\sigma^2 = 4 \left[ 1.42 - 0.1764 ight]$$\sigma^2 = 4 	imes 1.2436 = 4.9744 \approx 4.97$.

Marks of $A$	$30, 20, 40$
Marks of $B$	$70, 0, 5$

Find the variance of the following frequency distribution.

$Class$ $0-2$ $2-4$ $4-6$ $6-8$ $8-10$ $10-12$

$f_i$ $2$ $7$ $12$ $19$ $9$ $1$

Similar Questions

The variance of $20$ observations is $5$. If each observation is multiplied by $2$,find the new variance of the resulting observations.

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:

Marks of $A$ $30, 20, 40$

Marks of $B$ $70, 0, 5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

The mean of $5$ observations is $15$ and variance is $9$. If two observations having values $-5$ and $13$ are combined with these observations,then what will be the new variance?

For a set of $50$ observations,the sum of their squares is $3050$ and their arithmetic mean is $6$. Find the standard deviation of these observations.

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Find the variance of the following frequency distribution. $Class$ $0-2$ $2-4$ $4-6$ $6-8$ $8-10$ $10-12$ $f_i$ $2$ $7$ $12$ $19$ $9$ $1$