If the variance of the numbers $-1, 0, 1, k$ is $5$,where $k > 0$,then $k$ is equal to

  • A
    $2 \sqrt{\frac{10}{3}}$
  • B
    $2 \sqrt{6}$
  • C
    $4 \sqrt{\frac{5}{3}}$
  • D
    $\sqrt{6}$

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For the following frequency distribution,the variance is approximately equal to
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Frequency$4$$1$$10$$3$$2$

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If $\sum_{i=1}^{n}(x_{i}-a)=n$ and $\sum_{i=1}^{n}(x_{i}-a)^{2}=na$,where $n, a > 1$,then the standard deviation of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ is

Consider the following frequency distribution:
$C$.$I$.$75$-$175$$175$-$275$$275$-$375$$375$-$475$$475$-$575$$575$-$675$$675$-$775$
$f_i$$3$$2$$1$$0$$1$$2$$3$
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If both the mean and the standard deviation of $50$ observations $x_1, x_2, \dots, x_{50}$ are equal to $16$,then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, \dots, (x_{50} - 4)^2$ is

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