Practice Mean Absolute Deviation (MAD) in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The Mean Absolute Deviation (MAD) is the average of the absolute distances between each data point and the mean of the dataset. It measures how spread out data values are from the center, with larger MAD values indicating more variability.

Find how far each number is from the mean (ignoring +/-), then average those distances. It tells you: on average, how far is a typical value from the center?

Showing a random 20 of 76 problems.

Example 1

medium
The heights (in cm) of 6 plants are: 12, 15, 14, 18, 13, 16. Calculate the MAD and interpret the result in context.

Example 2

easy
MAD is always greater than or equal to ____.

Example 3

medium
Each value in a set is multiplied by 44. The original MAD was 2.52.5. What is the new MAD?

Example 4

easy
Find the MAD of 2,4,4,4,62, 4, 4, 4, 6.

Example 5

medium
Find the MAD of 3,5,7,93, 5, 7, 9.

Example 6

hard
A set of nn identical values cc has MAD 00. Add one new value vโ‰ cv \ne c. What is the new MAD?

Example 7

hard
A data set has MAD =5= 5. After dividing every value by 55, find the new MAD.

Example 8

medium
How does MAD differ from standard deviation conceptually?

Example 9

medium
MAD has the same units as which quantity?

Example 10

hard
A teacher claims that adding the same constant to every value in a data set does not change the MAD. Test this claim with the data set {5, 10, 15, 20, 25} by adding 100 to each value and comparing the MADs.

Example 11

medium
Two data sets: A = {10, 10, 10, 10, 10} and B = {2, 6, 10, 14, 18}. Both have a mean of 10. Calculate the MAD for each and explain what it tells you.

Example 12

medium
MAD is which type of statistic: measure of center or measure of spread?

Example 13

medium
A class has temperatures 68,70,72,70,7068, 70, 72, 70, 70 (โˆ˜^\circF). Find the MAD.

Example 14

medium
Data 1,2,3,4,1001, 2, 3, 4, 100 has mean 2222. Find the MAD.

Example 15

medium
Each value in a set is increased by 55. What happens to the MAD?

Example 16

hard
Find the MAD of 1,2,3,4,5,6,7,8,9,101, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Example 17

hard
Find the MAD of 2,4,4,4,5,5,7,92, 4, 4, 4, 5, 5, 7, 9.

Example 18

hard
Set S={2,4,6,8,10}S = \{2, 4, 6, 8, 10\} has mean 66. Replace 1010 with 2020. By how much does the MAD change?

Example 19

medium
If every value in a data set has 55 added to it, the MAD ____.

Example 20

hard
A data set {a,b}\{a, b\} with a<ba < b and mean m=(a+b)/2m = (a+b)/2 has MAD equal to what expression?
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