If the mean and variance of the data $65,68,58,44$, $48,45,60, \alpha, \beta, 60$ where $\alpha>\beta$ are $56$ and $66.2$ respectively, then $\alpha^2+\beta^2$ is equal to

  • [JEE MAIN 2024]
  • A

    $6435$

  • B

    $6798$

  • C

    $6344$

  • D

    $4312$

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If the mean and variance of the frequency distribution

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$f_i$ $4$ $4$ $\alpha$ $15$ $8$ $\beta$ $4$ $5$

are $9$ and $15.08$ respectively, then the value of $\alpha^2+\beta^2-\alpha \beta$ is $............$.

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The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is

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Find the variance and standard deviation for the following data:

${x_i}$ $4$ $8$ $11$ $17$ $20$ $24$ $32$
${f_i}$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

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

  • [JEE MAIN 2019]

The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variation is.....$\%$