If the standard deviation of $0, 1, 2, 3, …..,9$ is $K$, then the standard deviation of $10, 11, 12, 13 …..19$ is

  • A

    $K$

  • B

    $K + 10$

  • C

    $K + \sqrt {10} $

  • D

    $10\ K$

Similar Questions

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]

In an experiment with $15$ observations on $x$, the following results were available $\sum {x^2} = 2830$, $\sum x = 170$. On observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is..

  • [AIEEE 2003]

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac {1}{2}$ each and the remaining $10$ items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac {4}{3}$ then $\left| d \right|$ equals

  • [JEE MAIN 2019]

The mean and variance of the marks obtained by the students in a test are $10$ and $4$ respectively. Later, the marks of one of the students is increased from $8$ to $12$ . If the new mean of the marks is $10.2.$ then their new variance is equal to :

  • [JEE MAIN 2023]

Find the mean and variance for the following frequency distribution.

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