For the frequency distribution :

Variate $( x )$ $x _{1}$ $x _{1}$ $x _{3} \ldots \ldots x _{15}$
Frequency $(f)$ $f _{1}$ $f _{1}$ $f _{3} \ldots f _{15}$

where $0< x _{1}< x _{2}< x _{3}<\ldots .< x _{15}=10$ and

$\sum \limits_{i=1}^{15} f_{i}>0,$ the standard deviation cannot be 

  • [JEE MAIN 2020]
  • A

    $2$

  • B

    $1$

  • C

    $4$

  • D

    $6$

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

Marks $10-20$ $20-30$ $30-40$ $40-50$ $50-60$ $60-70$ $70-80$
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Group $B$ $10$ $20$ $30$ $25$ $43$ $15$ $7$

The $S.D$. of the first $n$ natural numbers is

The variance of first $50$ even natural numbers is

  • [JEE MAIN 2014]