The mean and variance of n observations x_1, | vedclass

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(D) The variance of $n$ observations is given by the formula $\sigma^2 = \frac{1}{n} \sum_{i=1}^n x_i^2 - (\bar{x})^2$,where $\bar{x}$ is the mean of

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$16$

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(D) The variance of $n$ observations is given by the formula $\sigma^2 = \frac{1}{n} \sum_{i=1}^n x_i^2 - (\bar{x})^2$,where $\bar{x}$ is the mean of the observations.Given that the mean $\bar{x} = 5$,variance $\sigma^2 = 0$,and $\sum_{i=1}^n x_i^2 = 400$.Substituting these values into the formula:$0 = \frac{1}{n}(400) - (5)^2$$0 = \frac{400}{n} - 25$$\frac{400}{n} = 25$$n = \frac{400}{25} = 16$Thus,the value of $n$ is $16$.

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
$f_i$	$3$	$7$	$12$	$15$	$8$	$3$	$2$

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

The mean and variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$ are $5$ and $0$ respectively. If $\sum_{i=1}^n x_i^2 = 400$,then the value of $n$ is equal to

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Find the mean and variance for the first $n$ natural numbers.

The standard deviation of the numbers $22, 26, 28, 20, 24, 30$ is

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

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

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

$f_i$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

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 $.69$)

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