If the variance of the first $n$ natural numbers is $10$ and the variance of the first m even natural numbers is $16$, then $m + n$ is equal to
If the variance of the first $n$ natural numbers is $10$ and the variance of the first m even natural numbers is $16$, then $m + n$ is equal to
- [JEE MAIN 2020]
- A
$16$
- B
$18$
- C
$24$
- D
$22$
Similar Questions
The mean and variance of eight observations are $9$ and $9.25,$ respectively. If six of the observations are $6,7,10,12,12$ and $13,$ find the remaining two observations.
The mean and variance of eight observations are $9$ and $9.25,$ respectively. If six of the observations are $6,7,10,12,12$ and $13,$ find the remaining two observations.
The varience of data $1001, 1003, 1006, 1007, 1009, 1010$ is -
The varience of data $1001, 1003, 1006, 1007, 1009, 1010$ is -
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
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
- [JEE MAIN 2023]
The variance $\sigma^2$ of the data is $ . . . . . .$
$x_i$
$0$
$1$
$5$
$6$
$10$
$12$
$17$
$f_i$
$3$
$2$
$3$
$2$
$6$
$3$
$3$
The variance $\sigma^2$ of the data is $ . . . . . .$
| $x_i$ | $0$ | $1$ | $5$ | $6$ | $10$ | $12$ | $17$ |
| $f_i$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
- [JEE MAIN 2024]
For a statistical data $x _1, x _2, \ldots, x _{10}$ of $10$ values, a student obtained the mean as $5.5$ and $\sum_{i=1}^{10} x _{ i }^2=371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$ , instead of the correct values $6$ and $8$ , respectively. The variance of the corrected data is
- [JEE MAIN 2025]