If the mean of the frequency distribution
Class: | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
Frequency | $2$ | $3$ | $x$ | $5$ | $4$ |
is $28$ , then its variance is $........$.
$150$
$152$
$153$
$151$
If the variance of the frequency distribution is $3$ then $\alpha$ is ......
$X_i$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
Frequency $f_i$ | $3$ | $6$ | $16$ | $\alpha$ | $9$ | $5$ | $6$ |
Find the standard deviation of the first n natural numbers.
Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$
The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1, 3$ and $8$, then a ratio of other two observations is
The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3 .$ If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44}$, then the standard deviation of the second sample is: