If the variance of the frequency distribution is $3$ then $\alpha$ is ......
$X_i$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
Frequency $f_i$ | $3$ | $6$ | $16$ | $\alpha$ | $9$ | $5$ | $6$ |
$5$
$4$
$3$
$2$
Let $x_1, x_2, x_3, x_4, .......... , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.
Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ......, 2x_n$ is $4\sigma ^2$ .
Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ......, 2x_n$ is $4\bar x$ .
Let the mean and standard deviation of marks of class $A$ of $100$ students be respectively $40$ and $\alpha( > 0)$, and the mean and standard deviation of marks of class $B$ of $n$ students be respectively $55$ and $30-\alpha$. If the mean and variance of the marks of the combined class of $100+ n$ students are respectively $50$ and $350$,then the sum of variances of classes $A$ and $B$ is
The mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$. If $M$ is the mean deviation of the numbers about the mean, then $25\; M$ is equal to
Let $x_1,x_2,.........,x_{100}$ are $100$ observations such that $\sum {{x_i} = 0,\,\sum\limits_{1 \leqslant i \leqslant j \leqslant 100} {\left| {{x_i}{x_j}} \right|} } = 80000\,\& $ mean deviation from their mean is $5,$ then their standard deviation, is-
In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals