Mean Absolute Deviation Mean Absolute Deviation O Definition: Mean - - PowerPoint PPT Presentation

Mean Absolute Deviation

Mean Absolute Deviation

O Definition: Mean Absolute Deviation (MAD) is

the average of absolute differences between each value in a set of values, and the average

• f all values of that set.

O The MAD measures the average (absolute)

distance of the sample values from the mean

• f the data values.

O Let x = data values O Let 𝒚

= mean.

Mean Absolute Deviation

O For example, the average (or mean) of

the set of values 1, 2, 3, 4, and 5 is (15 ÷ 5) or 3. The difference between this average (3) and the values in the set is 2, 1, 0, -1, and -2; the absolute difference being 2, 1, 0, 1, and 2. The average of these numbers (6 ÷ 5) is 1.2 which is the mean absolute deviation.

Find the Mean Absolute Deviation

Test scores for 6 students were : 85, 92, 88, 80, 91 and 20.

• 1. Find the me

mean an: (85+92+88+80+91+20)/6=76

• 2. Find the deviation

iation from m th the me mean an: 85-76=9 92-76=16 88-76=12 80-76=4 91-76=15 20-76=-56

Find the mean absolute deviation

Test scores for 6 students were : 85, 92, 88, 80, 91 and 20.

• 3. Find the absolute value of each

deviation from the mean:

85 76 9 92 76 16 88 76 12 80 76 4 91 76 15 20 76 56                 

Find the mean absolute deviation

Test scores for 6 students were : 85, 92, 88, 80, 91 and 20.

• 4. Find the sum of the absolute values:

9 + 16 + 12 + 4 + 15 + 56 = 112

• 5. Divide the sum by the number of

data items: 112/6 = 18.7 The me mean an ab absolu

• lute

e deviation viation is 18.7 18.7.

Steps for Finding MAD

• 1. Find the mean.
• 2. Subtract the sample mean from

each data value.

• 3. Take the absolute values of the

results.

• 4. Add the absolute values together.
• 5. Divide by the sample size.

MAD – Practice Problem What is the MAD for the following sample values? 3 8 6 12 0 -4 10

Use a Table

Data Values, x 𝒚 x– 𝒚 𝒚 − 𝒚 Total

MAD – Practice Problem Solution

MAD = 32/7 = 4.57