Question

a group of data items and their mean are given.
18, 30, 42, 72, 108, 162 ; mean = 72
a. find the deviation from the mean for each of the data items.
b. find the sum of the deviations in part (a).
a. type the deviation from the mean for each of the data items.
18 30 42 72 108 162
(simplify your answers.)

Explanation:

Step1: Calculate deviation for 18

Deviation = data item - mean. So, \(18 - 72=- 54\)

Step2: Calculate deviation for 30

\(30 - 72=-42\)

Step3: Calculate deviation for 42

\(42 - 72=-30\)

Step4: Calculate deviation for 72

\(72 - 72 = 0\)

Step5: Calculate deviation for 108

\(108 - 72=36\)

Step6: Calculate deviation for 162

\(162 - 72 = 90\)

Answer:

For part (a):

18	30	42	72	108	162

For part (b):
Sum of deviations: \((-54)+(-42)+(-30)+0 + 36+90=0\)