The variance of $20$ observations is $5$. If each observation is multiplied by $3$ and then $8$ is added to each number,then the variance of the resulting observations is:

  • A
    $35$
  • B
    $55$
  • C
    $25$
  • D
    $45$

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The variance of the following data is:
$x_i$ $6$ $10$ $14$ $18$ $24$ $28$ $30$
$f_i$ $2$ $4$ $7$ $12$ $8$ $4$ $3$

If each observation of a raw data whose variance is $\sigma^2$ is multiplied by $\lambda$,then the variance of the new set is

If the variance of four numbers $w, x, y,$ and $z$ is $9$,then the variance of $5w, 5x, 5y,$ and $5z$ is:

The following is the record of goals scored by team $A$ in a football session:
No. of goals scored $0, 1, 2, 3, 4$
No. of matches $1, 9, 7, 5, 3$

For team $B$,the mean number of goals scored per match was $2$ with a standard deviation of $1.25$ goals. Find which team may be considered more consistent?

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$A$ student scores the following marks in five tests: $54, 45, 41, 43, 57$. His score is not known for the sixth test. If the mean score is $48$ in six tests,then the standard deviation of marks in six tests is

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