x_i 6 10 14 18 24 28 30 f_i 2 4 7 12 8 4 3

NCERT Class XI Mathematics - Statistics - Solutions

Question : 16 of 34

Marks: +1, -0

$x_i$	6	10	14	18	24	28	30
$f_i$	2	4	7	12	8	4	3

Solution:

$x_i$	$f_i$	$f_i x_i$	$(x_i-19)$	$(x_i-19)^2$	$f_i (x_i-19)^2$
6	2	12	- 13	169	338
10	4	40	- 9	81	324
14	7	98	- 5	25	175
18	12	216	-1	1	12
24	8	192	5	25	200
28	4	112	9	81	324
30	3	90	11	121	363
	40	760			1736

Mean

(\overline{x})

\frac{1}{N} \sum\limits_{i=1}^{n} f_i x_i

\frac{1}{40}

× 760 = 19

Variance

(\sigma^2)

\frac{1}{N} \sum\limits_{i=1}^{n} f_i (x_i-\overline{x})^2

\frac{1}{40}

× 1736 = 43.4

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