If both the means and the standard deviation of $50$ observations $x_1, x_2, ………, x_{50}$ are equal to $16$ , then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, …., (x_{50} - 4)^2$ is

  • [JEE MAIN 2019]
  • A

    $400$

  • B

    $380$

  • C

    $525$

  • D

    $480$

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If the variance of the following frequency distribution is $50$ then $x$ is equal to:

Class $10-20$ $20-30$ $30-40$
Frequency $2$ $x$ $2$

  • [JEE MAIN 2020]

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$ be in $A.P.$ and $a_1+a_3=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to

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The mean and $S.D.$ of the marks of $200$ candidates were found to be $40$ and $15$ respectively. Later, it was discovered that a score of $40$ was wrongly read as $50$. The correct mean and $S.D.$ respectively are...

The variance of the first $n$ natural numbers is

From the data given below state which group is more variable, $A$ or $B$ ?

Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
Group $A$ $9$ $17$ $32$ $33$ $40$ $10$ $9$
Group $B$ $10$ $20$ $30$ $25$ $43$ $15$ $7$