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Question -

Find the mean and variance for the data 
6, 7, 10, 12, 13, 4, 8, 12



Answer -


So, x̅ = (6 + 7 + 10 + 12 + 13 + 4 + 8 + 12)/8
= 72/8
= 9
Let us make the table of the given data and append other columns after calculations.

Xi

Deviations from mean

(xi – x̅)

(xi – x̅)2

6

6 – 9 = -3

9

7

7 – 9 = -2

4

10

10 – 9 = 1

1

12

12 – 9 = 3

9

13

13 – 9 = 4

16

4

4 – 9 = – 5

25

8

8 – 9 = – 1

1

12

12 – 9 = 3

9

74

We know that Variance,

σ2 =(1/8) × 74

= 9.2

∴Mean = 9 and Variance= 9.25

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