Question

a group of data items and their mean are given.
12, 20, 28, 48, 72, 108 ; mean = 48
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.
12 20 28 48 72 108
(simplify your answers.)

Explanation:

Step1: Calculate deviation for 12

Deviation = data item - mean. So for \(12\), deviation is \(12 - 48=-36\)

Step2: Calculate deviation for 20

For \(20\), deviation is \(20 - 48=-28\)

Step3: Calculate deviation for 28

For \(28\), deviation is \(28 - 48=-20\)

Step4: Calculate deviation for 48

For \(48\), deviation is \(48 - 48 = 0\)

Step5: Calculate deviation for 72

For \(72\), deviation is \(72 - 48=24\)

Step6: Calculate deviation for 108

For \(108\), deviation is \(108 - 48 = 60\)

Answer:

• For \(12\): \(-36\)
• For \(20\): \(-28\)
• For \(28\): \(-20\)
• For \(48\): \(0\)
• For \(72\): \(24\)
• For \(108\): \(60\)