The variance and SD of the following is
$x$ $4.5$ $14.5$ $24.5$ $34.5$ $44.5$ $54.5$ $64.5$
$f$ $1$ $5$ $12$ $22$ $17$ $9$ $4$

176, 13

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175.9, 13.26

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8.56, 13

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4.1, 12.13

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Solution

The correct option is C $175.9, 13.26$
$¯ x = \frac{\sum F x}{\sum F} = \frac{2635}{70} = 37.64$
$σ^{2} = \frac{\sum F (x - ¯ x)^{2}}{\sum F} = \frac{12308.6}{70} = 175.9$
$∴ σ = 13.26$ .

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Similar questions

Q. Find the standard deviation for the following distribution:

x :	4.5	14.5	24.5	34.5	44.5	54.5	64.5
f :	1	5	12	22	17	9	4

Find the standard deviation for the following distribution :

$\begin{matrix} x : & 4.5 & 14.5 & 24.5 & 34.5 & 44.5 & 54.5 & 64.5 y : & 1 & 5 & 12 & 22 & 17 & 9 & 4 \end{matrix}$

Q. Find the variance of the following distribution.

Class interval	$3.5 - 4.5$	$4.5 - 5.5$	$5.5 - 6.5$	$6.5 - 7.5$	$7.5 - 8.5$
Frequency	$9$	$14$	$22$	$11$	$17$

A body released from a great height falls freely towards the earth.Another body is released from the same height exactly one second later. The separation between both the bodies two seconds after the release of the second body is

a) 24.5 metre

b)34.5 metre

c) 44.5 metre

d) 54.5 metre

Q. Find the variance and standard deviation of the following frequency distribution:

$x_{i}$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_{i}$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

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$x$	$4.5$	$14.5$	$24.5$	$34.5$	$44.5$	$54.5$	$64.5$
$f$	$1$	$5$	$12$	$22$	$17$	$9$	$4$

The variance and SD of the following isx4.514.524.534.544.554.564.5f1512221794

The correct option is C 175.9,13.26¯x=∑Fx∑F=263570=37.64σ2=∑F(x−¯x)2∑F=12308.670=175.9∴σ=13.26 .

The variance and SD of the following is
$x$ $4.5$ $14.5$ $24.5$ $34.5$ $44.5$ $54.5$ $64.5$
$f$ $1$ $5$ $12$ $22$ $17$ $9$ $4$

The correct option is C $175.9, 13.26$
$¯ x = \frac{\sum F x}{\sum F} = \frac{2635}{70} = 37.64$
$σ^{2} = \frac{\sum F (x - ¯ x)^{2}}{\sum F} = \frac{12308.6}{70} = 175.9$
$∴ σ = 13.26$ .