Practice Mean Absolute Deviation in Math

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

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Quick Recap

The average distance between each data value and the mean of the data set. Calculated by finding the mean, computing the absolute value of each deviation from the mean, and averaging those absolute deviations.

Standard deviation can feel abstract with its squaring and square roots. MAD is simpler: just ask 'on average, how far is each data point from the center?' If the mean test score is 80 and the MAD is 5, a typical student scored about 5 points away from 80β€”some above, some below.

Showing a random 20 of 50 problems.

Example 1

medium
Two basketball players average 20 points. Player A has MAD =2=2; Player B has MAD =9=9. Who is more consistent?

Example 2

medium
Data: 7,9,9,11,147, 9, 9, 11, 14. Compute the MAD.

Example 3

hard
A data set of 55 values has mean 2020 and sum of absolute deviations equal to 2525. Find the MAD.

Example 4

medium
Calculate the MAD of {10,12,14,16,18}\{10,12,14,16,18\} step by step.

Example 5

easy
The mean of a set is 1010. A data value is 77. What is its absolute deviation from the mean?

Example 6

easy
The absolute deviations of a 4-value set are 1,3,2,21, 3, 2, 2. Find the MAD.

Example 7

easy
A data set has 5 values. To compute MAD, you divide the sum of absolute deviations by what number?

Example 8

medium
Compute the MAD of {5,5,5,5,15}\{5,5,5,5,15\}.

Example 9

easy
Does MAD measure center or spread of a data set?

Example 10

hard
For a data set {a,b,c}\{a,b,c\} with mean 00, prove that the MAD equals ∣a∣+∣b∣+∣c∣3\tfrac{|a|+|b|+|c|}{3}.

Example 11

medium
Why is the sum of (signed) deviations from the mean always 00?

Example 12

hard
A four-value set {x,3,5,9}\{x,3,5,9\} has mean 55. Find xx and the MAD.

Example 13

medium
A 6-value set has absolute deviations 0,1,2,3,4,20, 1, 2, 3, 4, 2. Compute the MAD.

Example 14

challenge
A data set has mean ΞΌ\mu and MAD dd. After appending one new value ΞΌ\mu, what happens to the MAD?

Example 15

medium
Daily rainfall (in mm) for five days: {2,4,6,8,10}\{2,4,6,8,10\}. Find the MAD.

Example 16

challenge
Set A has values 10,10,10,1010, 10, 10, 10 (MAD 00). Set B has the same mean 1010 but values 4,8,12,164, 8, 12, 16. Compute B's MAD and state what differs between the sets.

Example 17

medium
If every value in a set is increased by 7, what happens to the MAD?

Example 18

challenge
Data set 2,4,4,4,5,5,7,92, 4, 4, 4, 5, 5, 7, 9 has mean 55. Compute the MAD.

Example 19

easy
Why must MAD use absolute values of deviations?

Example 20

challenge
For a data set {x1,x2,…,xn}\{x_1,x_2,\dots,x_n\}, show that the value mm that minimizes βˆ‘βˆ£xiβˆ’m∣\sum |x_i-m| is the median, not the mean.
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