Find the mean and standard deviation using ...

NCERT Class XI Mathematics - Statistics - Solutions

Question : 18 of 34

Marks: +1, -0

Find the mean and standard deviation using short-cut method.

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

Solution:

$x_i$	$f_i$	$u_i$ = $x_i-64$	$f_i u_i$	$f_i u_i^2$
60	2	-4	- 8	32
61	1	-3	- 3	9
62	12	- 2	- 24	48
63	29	- 1	-29	29
64	25	0	0	0
65	12	1	12	12
66	10	2	20	40
67	4	3	12	36
68	5	4	20	80
	100		0	286

Let assumed mean (A) = 64; Mean

\left(\overset{-}{x}\right)

= A +

\frac{\Sigma f_i u_i}{N}

= 64 +

\frac{0}{100}

= 64

S.D. (σ) =

\frac{1}{N} \sqrt{N \Sigma f_i u_i^2 - (\Sigma f_i u_i)^2}

\frac{1}{100} \sqrt{100 \times 286 - (0)^2}

\frac{1}{100} \sqrt{28600}

\frac{1}{100}

× 169.1 = 1.69

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