Find the mean and variance for the following | vedclass

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(A) 						Class			Frequency $f_i$			Mid-point $x_i$			$y_i = \frac{x_i - 25}{10}$			$f_i y_i$			$f_i y_i^2$							$0-10$			$5$			$5$			$-2$			$-10$

Vedclass · Accepted Answer

Mean = $27$,Variance = $132$

Vedclass · Answer

(A) 						Class			Frequency $f_i$			Mid-point $x_i$			$y_i = \frac{x_i - 25}{10}$			$f_i y_i$			$f_i y_i^2$							$0-10$			$5$			$5$			$-2$			$-10$			$20$							$10-20$			$8$			$15$			$-1$			$-8$			$8$							$20-30$			$15$			$25$			$0$			$0$			$0$							$30-40$			$16$			$35$			$1$			$16$			$16$							$40-50$			$6$			$45$			$2$			$12$			$24$							Total			$N = 50$			-			-			$\sum f_i y_i = 10$			$\sum f_i y_i^2 = 68$			Mean $\bar{x} = A + \left( \frac{\sum f_i y_i}{N} ight) 	imes h = 25 + \left( \frac{10}{50} ight) 	imes 10 = 25 + 2 = 27$.Variance $\sigma^2 = \frac{h^2}{N^2} [N \sum f_i y_i^2 - (\sum f_i y_i)^2] = \frac{10^2}{50^2} [50 	imes 68 - 10^2] = \frac{100}{2500} [3400 - 100] = \frac{1}{25} 	imes 3300 = 132$.

Find the mean and variance for the following frequency distribution.

Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$

Frequencies $5$ $8$ $15$ $16$ $6$

Similar Questions

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 $\frac{n(n + 1)(2n + 1)}{6}$.

Find the variance of the first $20$ natural numbers.

The variance of the first $50$ even natural numbers is

The variance of the first $20$ natural numbers is

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

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Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequencies	$5$	$8$	$15$	$16$	$6$

Find the mean and variance for the following frequency distribution. Classes $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ Frequencies $5$ $8$ $15$ $16$ $6$