The mean and the variance of five observation | vedclass

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(A) Let the five observations be $x_1, x_2, x_3, x_4, x_5$. Given $n = 5$,$\bar{x} = 4$,and $\sigma^2 = 5.2$.Sum of observations: $\sum x_i = n 	imes

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(A) Let the five observations be $x_1, x_2, x_3, x_4, x_5$. Given $n = 5$,$\bar{x} = 4$,and $\sigma^2 = 5.2$.Sum of observations: $\sum x_i = n 	imes \bar{x} = 5 	imes 4 = 20$.Given $x_1 = 3, x_2 = 4, x_3 = 4$,we have $3 + 4 + 4 + x_4 + x_5 = 20$,so $x_4 + x_5 = 9$ $(i)$.Variance formula: $\sigma^2 = \frac{\sum x_i^2}{n} - (\bar{x})^2$.$5.2 = \frac{\sum x_i^2}{5} - 4^2$ $\Rightarrow 5.2 = \frac{\sum x_i^2}{5} - 16$ $\Rightarrow \sum x_i^2 = 5 	imes 21.2 = 106$.Sum of squares: $3^2 + 4^2 + 4^2 + x_4^2 + x_5^2 = 106$ $\Rightarrow 9 + 16 + 16 + x_4^2 + x_5^2 = 106$ $\Rightarrow x_4^2 + x_5^2 = 65$ $(ii)$.We know $(x_4 - x_5)^2 = 2(x_4^2 + x_5^2) - (x_4 + x_5)^2$.$(x_4 - x_5)^2 = 2(65) - (9)^2 = 130 - 81 = 49$.Therefore,$|x_4 - x_5| = \sqrt{49} = 7$.

Class	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$2$	$k$	$28$	$54$	$k + 1$	$5$

Class	Frequency
$0 - 20$	$17$
$20 - 40$	$f_1$
$40 - 60$	$32$
$60 - 80$	$f_2$
$80 - 100$	$19$
Total	$120$

The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4,$ and $4,$ then the absolute value of the difference of the other two observations is

Similar Questions

If the mean of the data:
Class $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$
Frequency $2$ $k$ $28$ $54$ $k + 1$ $5$

is $21$,then $k$ is one of the roots of the equation:

The range of the observations $2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3$ is . . . . . . .

Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, 67$ $(a > b)$ are $40$ and $21$,respectively. If the mean deviation about the median is $26$,then $2a$ is equal to:

If the arithmetic mean of the following frequency distribution is $50$,find the values of $f_1$ and $f_2$.
Class Frequency
$0 - 20$ $17$
$20 - 40$ $f_1$
$40 - 60$ $32$
$60 - 80$ $f_2$
$80 - 100$ $19$
Total $120$

The average marks of boys in a class is $40$ and that of girls is $45$. The average marks of both boys and girls combined is $42$. Then the percentage of boys in the class is (in $\%$)

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