SME
Grade 6 Math · Problem type
Mean absolute deviation
Use this for “Find the mean absolute deviation of the data.”
Diagram
5 values in order: 4, 5, 7, 9, 10.
The median is the middle value, 7.
This is an example. Type your own values to start a new problem.
Number of values
example
First value
example
Second value
example
Third value
example
Fourth value
example
Fifth value
example
Mean
worked out (not typed)
Mean absolute deviation
worked out (not typed)
Formulas
sum of the 5 values ÷ 5 = 7
Sum of the values ÷ number of values = mean
mean distance from 7 of the 5 values: 2
Mean of the distances from the mean = mean absolute deviation
Assumptions
•
Find the mean first.
•
The distance of each value from the mean is never negative.
•
The MAD is the mean of those distances: a bigger MAD means the data is more spread out.
•
From 3 to 12 values.
Step-by-step
WE KNOW
Number of values: 5
First value: 4
Second value: 7
Third value: 9
Fourth value: 5
Fifth value: 10
FIND
mean, mean absolute deviation
Step 1 · Find mean
sum of the 5 values ÷ 5 = ?
Sum of the values ÷ number of values = mean
Add the values and share the sum equally among them.
4 + 7 + 9 + 5 + 10 = 35
35 ÷ 5 = 7
Mean = 7
Step 2 · Find mean absolute deviation
mean distance from 7 of the 5 values: ?
Mean of the distances from the mean = mean absolute deviation
Find how far each value is from the mean. Then find the mean of those distances.
Distances from 7: 3, 0, 2, 2, 3
3 + 0 + 2 + 2 + 3 = 10
10 ÷ 5 = 2
Mean absolute deviation = 2
Check
Put the numbers back in. Both sides should match.
(4 + 7 + 9 + 5 + 10) ÷ 5 = 7 ✓
mean distance from 7 of 4, 7, 9, 5, 10: 2 ✓
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