Question

1. 4,7, 8, 9, 10, 12, 13, 17

Answer 1

The given data is: 4, 7, 8, 9, 10, 12, 13, 17.

The formula to calculate the mean is the ratio of 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 =4+7+8+9+10+12+13+17 =80

Since the total number of observation is 8, thus substitute 8 for n and 80 for ∑ i=1 n x i in equation (1).

x ¯ = 1 8 ( 80 ) =10

Therefore, the mean of the given data is 10.

The formula to calculate the deviations of the respective observations of the data from the mean x ¯ is,

x ¯ − x i (2)

Substitute 10 for x ¯ and 4, 7, 8, 9, 10, 12, 13, 17 respectively for x i in equation (2).

−6, −3, −2, −1, 0, 2, 3, 7

The formula to calculate the absolute deviation of the respective observations of the data is,

| x ¯ − x i | (3)

Substitute −6, −3, −2, −1, 0, 2, 3, 7 for x ¯ − x i respectively in equation (3).

6, 3 ,2 1, 0, 2, 3, 7

The formula to calculate the mean deviation about the mean is the ratio of the sum of absolute values of deviations to the number of deviations.

M.D.= ∑ i=1 n | x ¯ − x i | n (4)

Substitute 8 for n and 6, 3 ,2 1, 0, 2, 3, 7 for | x ¯ − x i | respectively in equation (4).

M.D.= 6+3+2+1+0+2+3+7 8 =3

Thus, the mean deviation of the given data is 3.