Let the mean and variance of four numbers $3,7, x$ and $y(x>y)$ be $5$ and $10$ respectively. Then the mean of four numbers $3+2 \mathrm{x}, 7+2 \mathrm{y}, \mathrm{x}+\mathrm{y}$ and $x-y$ is ..... .

  • [JEE MAIN 2021]
  • A

    $10$

  • B

    $11$

  • C

    $12$

  • D

    $48$

Similar Questions

If each of given $n$ observations is multiplied by a certain positive number $'k'$, then for new set of observations -

The $S.D$ of $15$ items is $6$ and if each item is decreased or increased by $1$, then standard deviation will be

The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$

  Height Weight
Mean $162.6\,cm$ $52.36\,kg$
Variance $127.69\,c{m^2}$ $23.1361\,k{g^2}$

Can we say that the weights show greater variation than the heights?

The data is obtained in tabular form as follows.

${x_i}$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
${f_i}$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

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]