Question

2. 38,70, 48,40, 42,55, 63, 46, 54, 44

Answer 1

The given data is: 38, 70, 48, 40, 42,55, 63, 46, 54, 44.

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 =38+70+48+40+42+55+63+46+54+44 =500

Since the total number of observation is 10, thus substitute 10 for n and 500 for ∑ i=1 n x i in equation (1).

x ¯ = 1 10 ( 500 ) =50

Therefore, the mean of the given data is 50.

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

x ¯ − x i (2)

Substitute 50 for x ¯ and 38, 70, 48, 40, 42,55, 63, 46, 54, 44 respectively for x i in equation (2).

12, −20, 2, 10, 8, −5, −13, 4, −4, 6

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

| x ¯ − x i | (3)

Substitute 12, −20, 2, 10, 8, −5, −13, 4, −4, 6 for x ¯ − x i respectively in equation (3).

12, 20, 2, 10, 8, 5, 13, 4, 4, 6

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 10 for n and 12, 20, 2, 10, 8, 5, 13, 4, 4, 6 for | x ¯ − x i | respectively in equation (4).

M.D.= 12+20+2+10+8+5+13+4+4+6 10 =8.4

Thus, the mean deviation of the given data is 8.4.