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

    $6$

Similar Questions

Let $X _{1}, X _{2}, \ldots, X _{18}$ be eighteen observations such that $\sum_{ i =1}^{18}\left( X _{ i }-\alpha\right)=36 \quad$ and $\sum_{i=1}^{18}\left(X_{i}-\beta\right)^{2}=90,$ where $\alpha$ and $\beta$ are distinct real numbers. If the standard deviation of these observations is $1,$ then the value of $|\alpha-\beta|$ is ...... .

  • [JEE MAIN 2021]

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$.........$

  • [JEE MAIN 2022]

Let $X=\{\mathrm{x} \in \mathrm{N}: 1 \leq \mathrm{x} \leq 17\}$ and $\mathrm{Y}=\{\mathrm{ax}+\mathrm{b}: \mathrm{x} \in \mathrm{X}$ and $\mathrm{a}, \mathrm{b} \in \mathrm{R}, \mathrm{a}>0\} .$ If mean and variance of elements of $Y$ are $17$ and $216$ respectively then $a + b$ is equal to 

  • [JEE MAIN 2020]

The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Subject  Mathematics Physics Chemistty
Mean $42$ $32$ $40.9$
Standard deviation $12$ $15$ $20$

Which of the three subjects shows the highest variability in marks and which shows the lowest?

Find the variance and standard deviation for the following data:

${x_i}$ $4$ $8$ $11$ $17$ $20$ $24$ $32$
${f_i}$ $3$ $5$ $9$ $5$ $4$ $3$ $1$