The variance of the following frequency distr | vedclass

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(B) To find the variance,we first calculate the mid-values $(x_i)$ for each class and then compute $\Sigma f_i x_i$ and $\Sigma f_i x_i^2$.ClassMid va

Vedclass · Accepted Answer

$161.1$

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(B) To find the variance,we first calculate the mid-values $(x_i)$ for each class and then compute $\Sigma f_i x_i$ and $\Sigma f_i x_i^2$.ClassMid value $(x_i)$$f_i$$f_i x_i$$f_i x_i^2$$0-10$$5$$11$$55$$275$$10-20$$15$$29$$435$$6525$$20-30$$25$$18$$450$$11250$$30-40$$35$$4$$140$$4900$$40-50$$45$$5$$225$$10125$$50-60$$55$$3$$165$$9075$Total-$70$$1470$$42150$Here,$N = \Sigma f_i = 70$ and $\Sigma f_i x_i = 1470$.The mean $\bar{x} = \frac{\Sigma f_i x_i}{N} = \frac{1470}{70} = 21$.The variance $\sigma^2 = \frac{1}{N} \Sigma f_i x_i^2 - (\bar{x})^2$.$\sigma^2 = \frac{42150}{70} - (21)^2$.$\sigma^2 = 602.14 - 441 = 161.14$.Rounding to one decimal place,the variance is $161.1$.

The variance of the following frequency distribution is:
Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$
Frequency $11$ $29$ $18$ $4$ $5$ $3$

Similar Questions

Find the variance of the following frequency distribution.

$Class$ $0-2$ $2-4$ $4-6$ $6-8$ $8-10$ $10-12$

$f_i$ $2$ $7$ $12$ $19$ $9$ $1$

The variance of the following continuous frequency distribution is
Class Interval $0-10$ $10-20$ $20-30$ $30-40$
Frequency $2$ $3$ $4$ $1$

If $A$ and $B$ are the variances of the first $n$ even numbers and the first $n$ odd numbers respectively,then:

The standard deviation of $7$ observations $1, 2, 3, 4, 5, 6, 7$ is:

Calculate the variance if $\Sigma x_i^2 = 18000$ and $\Sigma x_i = 960$,for $60$ observations.

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Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$11$	$29$	$18$	$4$	$5$	$3$

Class Interval	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$2$	$3$	$4$	$1$

The variance of the following frequency distribution is:Classes$0-10$$10-20$$20-30$$30-40$$40-50$$50-60$Frequency$11$$29$$18$$4$$5$$3$