The mean of the values sin^2 10^{circ}, sin^2 | vedclass

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(A) The given values are $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \dots, \sin^2 90^{\circ}$.There are $9$ terms in total.Sum $= \sin^

Vedclass · Accepted Answer

$\frac{5}{9}$

Vedclass · Answer

(A) The given values are $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \dots, \sin^2 90^{\circ}$.There are $9$ terms in total.Sum $= \sin^2 10^{\circ} + \sin^2 20^{\circ} + \sin^2 30^{\circ} + \sin^2 40^{\circ} + \sin^2 50^{\circ} + \sin^2 60^{\circ} + \sin^2 70^{\circ} + \sin^2 80^{\circ} + \sin^2 90^{\circ}$.Using $\sin(90^{\circ} - 	heta) = \cos 	heta$,we have $\sin^2 80^{\circ} = \cos^2 10^{\circ}$,$\sin^2 70^{\circ} = \cos^2 20^{\circ}$,$\sin^2 60^{\circ} = \cos^2 30^{\circ}$,and $\sin^2 50^{\circ} = \cos^2 40^{\circ}$.Sum $= (\sin^2 10^{\circ} + \cos^2 10^{\circ}) + (\sin^2 20^{\circ} + \cos^2 20^{\circ}) + (\sin^2 30^{\circ} + \cos^2 30^{\circ}) + (\sin^2 40^{\circ} + \cos^2 40^{\circ}) + \sin^2 90^{\circ}$.Since $\sin^2 	heta + \cos^2 	heta = 1$ and $\sin 90^{\circ} = 1$,Sum $= 1 + 1 + 1 + 1 + (1)^2 = 5$.Mean $= \frac{	ext{Total Sum}}{	ext{Number of terms}} = \frac{5}{9}$.

Class	Frequency
$10-20$	$180$
$20-30$	$82$
$30-40$	$34$
$40-50$	$180$
$50-60$	$136$
$60-70$	$23$
$70-80$	$50$

$x_i$	$5$	$8$	$11$	$14$	$17$
$f_i$	$4$	$5$	$6$	$10$	$20$

The mean of the values $\sin^2 10^{\circ}, \sin^2 20^{\circ}, \sin^2 30^{\circ}, \ldots, \sin^2 90^{\circ}$ is $........$

Similar Questions

Find the median for the following distribution:
Class Frequency
$10-20$ $180$
$20-30$ $82$
$30-40$ $34$
$40-50$ $180$
$50-60$ $136$
$60-70$ $23$
$70-80$ $50$

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$x_i$ $5$ $8$ $11$ $14$ $17$

$f_i$ $4$ $5$ $6$ $10$ $20$

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