Question

1.6,7, 10, 12, 13, 4, 8, 12

Answer 1

The given data is: 6, 7, 10, 12, 13, 4, 8, 12.

The formula to calculate the mean is the ratio of the sum of observations to the number of observations.

x ¯ = 1 n ∑ i=1 n x i (1)

The sum of observations is,

∑ i=1 n x i =6+7+10+12+13+4+8+12 =72

Since the total number of observation is 8, thus substitute 8 for n and 72 for ∑ i=1 n x i in equation (1).

x ¯ = 1 8 ( 72 ) =9

Therefore, the mean of the given data is 9.

The formula to calculate the variance is,

σ 2 = 1 n ∑ i=1 n ( x i − x ¯ ) 2 (2)

Substitute 9 for x ¯ and 6, 7, 10, 12, 13, 4, 8, 12 for x i respectively in x i − x ¯ and make a table to evaluate the variance.

x i	x i − x ¯	( x i − x ¯ ) 2
6	−3	9
7	−2	4
10	−1	1
12	3	9
13	4	16
4	−5	25
8	−1	1
12	3	9
∑ i=1 n x i =72		∑ i=1 n ( x i − x ¯ ) 2 =74

Substitute 8 for n and 74 for ∑ i=1 n ( x i − x ¯ ) 2 in equation (2).

σ 2 = 74 8 =9.25

Thus, the variance of the given data is 9.25.