The standard deviation of a, a+d, a+2 d, ldot | vedclass

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Question

(C) The given series is an arithmetic progression: $a, a+d, a+2d, \ldots, a+2nd$.The number of terms $m$ is given by $a+(m-1)d = a+2nd$,which implies

Vedclass · Accepted Answer

$\sqrt{\frac{n(n+1)}{3}} d$

Vedclass · Answer

(C) The given series is an arithmetic progression: $a, a+d, a+2d, \ldots, a+2nd$.The number of terms $m$ is given by $a+(m-1)d = a+2nd$,which implies $m-1 = 2n$,so $m = 2n+1$.The standard deviation $\sigma$ of an arithmetic progression with $m$ terms and common difference $d$ is given by the formula $\sigma = \sqrt{\frac{m^2-1}{12}} |d|$.Substituting $m = 2n+1$:$\sigma = \sqrt{\frac{(2n+1)^2-1}{12}} |d|$$\sigma = \sqrt{\frac{4n^2+4n+1-1}{12}} |d|$$\sigma = \sqrt{\frac{4n(n+1)}{12}} |d|$$\sigma = \sqrt{\frac{n(n+1)}{3}} |d|$Thus,the correct option is $C$.

Marks	$1-3$	$3-5$	$5-7$	$7-9$
Number of students	$40$	$30$	$20$	$10$

	Section $A$	Section $B$
Number of students	$50$	$60$
Average marks in the test	$45$	$45$
Variance of distribution of marks	$64$	$81$

The standard deviation of $a, a+d, a+2 d, \ldots, a+2 n d$ is

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If the sum of squares of deviations of $10$ observations from their mean $50$ is $250$,what is the coefficient of variation?

The variance of the following distribution is:
Marks $1-3$ $3-5$ $5-7$ $7-9$
Number of students $40$ $30$ $20$ $10$

Find the variance of the sequence $a, a + d, a + 2d, \dots, a + 2nd$.

Students of two sections $A$ and $B$ of a class show the following results in a test conducted for $100$ marks. Then

Section $A$ Section $B$

Number of students $50$ $60$

Average marks in the test $45$ $45$

Variance of distribution of marks $64$ $81$

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