(D) The standard deviation $(\sigma)$ for a frequency distribution is given by the formula: $\sigma = \sqrt{\frac{\sum f_i d_i^2}{N} - \left(\frac{\su

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$\sigma = \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd}{\sum f}\right)^2}$

(D) The standard deviation $(\sigma)$ for a frequency distribution is given by the formula: $\sigma = \sqrt{\frac{\sum f_i d_i^2}{N} - \left(\frac{\sum f_i d_i}{N}\right)^2}$ where $N = \sum f_i$ and $d_i = x_i - A$ (the deviation from the assumed mean). Thus,the correct formula is option $D$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

For a frequency distribution,the standard deviation is computed by applying the formula:

A
$\sigma = \sqrt{\left(\frac{\sum fd}{\sum f}\right) - \frac{\sum fd^2}{\sum f}}$
B
$\sigma = \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd^2}{\sum f}\right)^2}$
C
$\sigma = \sqrt{\left(\frac{\sum fd}{\sum f}\right)^2 - \frac{\sum fd^2}{\sum f}}$
D
$\sigma = \sqrt{\frac{\sum fd^2}{\sum f} - \left(\frac{\sum fd}{\sum f}\right)^2}$

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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Statistics

Subtopic

Variance and Standard Deviation

The variance of the numbers $8, 21, 34, 47, \ldots, 320$ is . . . . . . .

MediumJEE MAIN 2025

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From the prices of shares $X$ and $Y$ below,find out which is more stable in value:

$X$ $35$ $54$ $52$ $53$ $56$ $58$ $52$ $50$ $51$ $49$

$Y$ $108$ $107$ $105$ $105$ $106$ $107$ $104$ $103$ $104$ $101$

Difficult

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In a discrete data,$\frac{1}{4}$ of the observations are equal to $a$,another $\frac{1}{4}$ of the observations are equal to $-a$. Out of the remaining,half of them are equal to $b$ and the rest are equal to $-b$. If the variance of all the observations is $ab$,then:

MediumTS EAMCET 2020

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Statement $1$: The variance of the first $n$ odd natural numbers is $\frac{n^2 - 1}{3}$.
Statement $2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.

DifficultAIEEE 2012

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If each observation of a raw data whose variance is $\sigma^2$ is multiplied by $\lambda$,then the variance of the new set is

Medium

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$X$	$35$	$54$	$52$	$53$	$56$	$58$	$52$	$50$	$51$	$49$
$Y$	$108$	$107$	$105$	$105$	$106$	$107$	$104$	$103$	$104$	$101$

For a frequency distribution,the standard deviation is computed by applying the formula:

Similar Questions

The variance of the numbers $8, 21, 34, 47, \ldots, 320$ is . . . . . . .

From the prices of shares $X$ and $Y$ below,find out which is more stable in value: $X$ $35$ $54$ $52$ $53$ $56$ $58$ $52$ $50$ $51$ $49$ $Y$ $108$ $107$ $105$ $105$ $106$ $107$ $104$ $103$ $104$ $101$

In a discrete data,$\frac{1}{4}$ of the observations are equal to $a$,another $\frac{1}{4}$ of the observations are equal to $-a$. Out of the remaining,half of them are equal to $b$ and the rest are equal to $-b$. If the variance of all the observations is $ab$,then:

Statement $1$: The variance of the first $n$ odd natural numbers is $\frac{n^2 - 1}{3}$.Statement $2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.

If each observation of a raw data whose variance is $\sigma^2$ is multiplied by $\lambda$,then the variance of the new set is

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From the prices of shares $X$ and $Y$ below,find out which is more stable in value:

$X$ $35$ $54$ $52$ $53$ $56$ $58$ $52$ $50$ $51$ $49$

$Y$ $108$ $107$ $105$ $105$ $106$ $107$ $104$ $103$ $104$ $101$

Statement $1$: The variance of the first $n$ odd natural numbers is $\frac{n^2 - 1}{3}$.
Statement $2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.