The data is obtained in tabular form as follo | vedclass

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(A) Let $A = 64$ and $h = 1$. We define $y_i = \frac{x_i - 64}{1}$.$x_i$$f_i$$y_i$$f_i y_i$$f_i y_i^2$$60$$2$$-4$$-8$$32$$61$$1$$-3$$-3$$9$$62$$12$$-2

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(A) Let $A = 64$ and $h = 1$. We define $y_i = \frac{x_i - 64}{1}$.$x_i$$f_i$$y_i$$f_i y_i$$f_i y_i^2$$60$$2$$-4$$-8$$32$$61$$1$$-3$$-3$$9$$62$$12$$-2$$-24$$48$$63$$29$$-1$$-29$$29$$64$$25$$0$$0$$0$$65$$12$$1$$12$$12$$66$$10$$2$$20$$40$$67$$4$$3$$12$$36$$68$$5$$4$$20$$80$Total$N=100$-$\sum f_i y_i = 0$$\sum f_i y_i^2 = 286$Mean $\bar{x} = A + \frac{\sum f_i y_i}{N} 	imes h = 64 + \frac{0}{100} 	imes 1 = 64$.Variance $\sigma^2 = \frac{h^2}{N^2} [N \sum f_i y_i^2 - (\sum f_i y_i)^2] = \frac{1^2}{100^2} [100 	imes 286 - 0^2] = \frac{28600}{10000} = 2.86$.Standard deviation $\sigma = \sqrt{2.86} \approx 1.69$.

Classes	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency $({f_i})$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

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

The data is obtained in tabular form as follows:
$x_i$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$
$f_i$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$

Find the standard deviation of the given data. (in $.69$)

Similar Questions

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

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

Frequency $({f_i})$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

The arithmetic mean and standard deviation of a data set of nine numbers are $13$ and $5$ respectively. If $3$ is included as the $10^{th}$ item of the data,then the variance of the data set of ten numbers is:

The raw data $x_1, x_2, \ldots, x_{n}$ is an $A$.$P$. with common difference $d$ and first term $0$. If $\bar{x}$ and $\sigma^2$ are the mean and variance of $x_{i}, i=1, 2, \ldots, n$,then $\sigma^2$ is:

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 $64$ $81$

The $S.D.$ of $15$ items is $6$. If each item is decreased or increased by $1$,then the standard deviation will be:

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$x_i$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
$f_i$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

The data is obtained in tabular form as follows:$x_i$$60$$61$$62$$63$$64$$65$$66$$67$$68$$f_i$$2$$1$$12$$29$$25$$12$$10$$4$$5$Find the standard deviation of the given data. (in $.69$)