If both the means and the standard deviation of $50$ observations $x_1, x_2, ………, x_{50}$ are equal to $16$ , then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, …., (x_{50} - 4)^2$ is
$400$
$380$
$525$
$480$
If the variance of the following frequency distribution is $50$ then $x$ is equal to:
Class | $10-20$ | $20-30$ | $30-40$ |
Frequency | $2$ | $x$ | $2$ |
Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to
The mean and $S.D.$ of the marks of $200$ candidates were found to be $40$ and $15$ respectively. Later, it was discovered that a score of $40$ was wrongly read as $50$. The correct mean and $S.D.$ respectively are...
The variance of the first $n$ natural numbers is
From the data given below state which group is more variable, $A$ or $B$ ?
Marks | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $60-70$ | $70-80$ |
Group $A$ | $9$ | $17$ | $32$ | $33$ | $40$ | $10$ | $9$ |
Group $B$ | $10$ | $20$ | $30$ | $25$ | $43$ | $15$ | $7$ |