(D) The percentage increase of a value $B$ over a value $A$ is given by the formula: $\frac{B-A}{A} \times 100$.Here,we need to find the percentage in

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$\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100$

(D) The percentage increase of a value $B$ over a value $A$ is given by the formula: $\frac{B-A}{A} \times 100$.Here,we need to find the percentage increase in the standard deviation of $D_2$ $(\sigma_2)$ over the standard deviation of $D_1$ $(\sigma_1)$.Therefore,the required percentage increase is $\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Easy

Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

TS EAMCET 2018 All TS EAMCET

A
$\frac{\sigma_1-\sigma_2}{\sigma_2} \times 100$
B
$\frac{\sigma_1-\sigma_2}{\sigma_1} \times 100$
C
$\frac{\sigma_2-\sigma_1}{\sigma_2} \times 100$
D
$\frac{\sigma_2-\sigma_1}{\sigma_1} \times 100$

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Variance and Standard Deviation

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TS EAMCET 2018 Paper All TS EAMCET years →

If the standard deviation of the numbers $2, 3, 2x$,and $11$ is $3.5$,find the possible values of $x$.

EasyAP EAMCET 2020

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Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?

EasyJEE MAIN 2021

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The variance of the following frequency distribution is:
Class Interval $0$-$4$ $4$-$8$ $8$-$12$ $12$-$16$ $16$-$20$
Frequency $2$ $4$ $6$ $3$ $1$

MediumTS EAMCET 2019

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

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$

$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

Difficult

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Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{4}$.
Statement-$2$: The sum of the first $n$ natural numbers is $\frac{n(n + 1)}{2}$ and the sum of the squares of the first $n$ natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$.

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Class Interval	$0$-$4$	$4$-$8$	$8$-$12$	$12$-$16$	$16$-$20$
Frequency	$2$	$4$	$6$	$3$	$1$

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

Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

Similar Questions

If the standard deviation of the numbers $2, 3, 2x$,and $11$ is $3.5$,find the possible values of $x$.

Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?

The variance of the following frequency distribution is:Class Interval$0$-$4$$4$-$8$$8$-$12$$12$-$16$$16$-$20$Frequency$2$$4$$6$$3$$1$

Calculate the mean,variance,and standard deviation for the following distribution: Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$ $f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{4}$.Statement-$2$: The sum of the first $n$ natural numbers is $\frac{n(n + 1)}{2}$ and the sum of the squares of the first $n$ natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$.

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The variance of the following frequency distribution is:
Class Interval $0$-$4$ $4$-$8$ $8$-$12$ $12$-$16$ $16$-$20$
Frequency $2$ $4$ $6$ $3$ $1$

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

Class $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$

$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

Statement-$1$: The variance of the first $n$ even natural numbers is $\frac{n^2 - 1}{4}$.
Statement-$2$: The sum of the first $n$ natural numbers is $\frac{n(n + 1)}{2}$ and the sum of the squares of the first $n$ natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$.