For a frequency distribution, standard deviation is computed by

  • A
    $\sigma = \frac{{\sum f(x - \bar x)}}{{\sum f}}$
  • B
    $\sigma = \frac{{\sqrt {\sum f{{(x - \bar x)}^2}} }}{{\sum f}}$
  • C
    $\sigma = \sqrt {\frac{{\sum f{{(x - \bar x)}^2}}}{{\sum f}}} $
  • D
    $\sigma = \sqrt {\frac{{\sum f(x - \bar x)}}{{\sum f}}} $

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Let the mean and variance of $8$ numbers $x , y , 10$, $12,6,12,4,8$, be $9$ and $9.25$ respectively. If $x > y$, then $3 x-2 y$ is equal to $...........$.

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Suppose a class has $7$ students. The average marks of these students in the mathematics examination is $62$, and their variance is $20$ . A student fails in the examination if $he/she$ gets less than $50$ marks, then in worst case, the number of students can fail is

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The variance of first $50$ even natural numbers is

Calculate the mean, variance and standard deviation for the following distribution:

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

Find the mean and variance for the following frequency distribution.

Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$
Frequencies $5$ $8$ $15$ $16$ $6$