8C Mean Absolute Deviation Study Guide

Key Vocabulary

Mean Absolute Deviation (MAD) — the average distance each data value is from the mean. It measures how spread out data is. (desviación media absoluta)

Absolute Value — the distance a number is from zero; always positive or zero. Written as |n|. (valor absoluto)

Deviation — how far a data value is from the mean. (desviación)

Spread — how spread out or close together the data values are. (dispersión)

Step-by-Step: Calculate MAD

1 Find the mean of the data set (add all values, divide by count).
2 Find each deviation — subtract the mean from each value (value − mean).
3 Take the absolute value of each deviation (make them all positive).
4 Find the mean of the absolute deviations (add them up, divide by count).

Worked Example

Data set: {2, 4, 6, 8, 10}

Step 1: Mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6

Value	Value − Mean	\|Deviation\|
2	2 − 6 = −4	4
4	4 − 6 = −2	2
6	6 − 6 = 0	0
8	8 − 6 = 2	2
10	10 − 6 = 4	4

Step 4: MAD = (4 + 2 + 0 + 2 + 4) ÷ 5 = 12 ÷ 5 = 2.4

This means each value is, on average, 2.4 units away from the mean.

Formula Box

MAD = Sum of |each value − mean| ÷ number of values

Small MAD = data is close together | Large MAD = data is spread out

Watch Out!

Absolute value means ALWAYS positive. Even if the deviation is negative, you make it positive before averaging.
MAD can never be negative. It measures distance, and distance is always 0 or more.
Don't skip finding the mean first! You need the mean before you can find deviations.
MAD tells you about spread, not center. Mean and median tell you about center.

Practice Problems

Use this data set: {3, 5, 7, 9, 11}

1. What is the mean of {3, 5, 7, 9, 11}?

2. What is the absolute deviation of the value 3 from the mean? (|3 − mean|)

3. What is the absolute deviation of the value 9 from the mean? (|9 − mean|)