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$.

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

Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{4}$.
Statement-$2$: The sum of the first $n$ natural numbers is $\frac{n(n + 1)}{2}$ and the sum of the squares of the first $n$ natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$.

The mean of $100$ observations is $50$ and their standard deviation is $5$. Then,the sum of squares of all observations is

The variance of the first $n$ natural numbers is

If $v$ is the variance and $\sigma$ is the standard deviation,then

The coefficient of variation for the frequency distribution is
$x_i$ $4$ $3$ $1$
$f_i$ $1$ $3$ $5$

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