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Q.

The variance of the following data
$x_{i}$ 1 2 3 4 5 6 7 8 9 10
$⨍_{i}$ 1 2 3 4 5 6 7 8 9 10

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a

8

b

10

c

9

d

6

answer is D.

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Detailed Solution

$x_{i}$	1	2	3	4	5	6	7	8	9	10
$⨍_{i}$	1	2	3	4	5	6	7	8	9	10
$f_{i} x_{i}$	1	4	9	16	25	36	49	64	81	100
$(x_{i} - x)$	6	5	4	3	2	1	0	1	2	3
$f_{i} {(x_{i} - x)}^{2}$	36	50	48	36	20	6	0	8	36	90

$\begin{array}{rcl} \sum f_{i} & = & 55, x = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{10 \times 11 \times 21}{55 \times 6} = 7 \\ σ^{2} & = & \frac{\sum f_{i} {(x_{i} - x)}^{2}}{\sum f_{i}} \\ = & \frac{36 + 50 + 48 + 36 + 20 + 6 + 8 + 36 + 90}{55} \\ = & \frac{330}{55} = 6 \end{array}$

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