Mean Absolute Deviation- 7th Grade Worksheets and Practice

What Is Mean Absolute Deviation?

Mean Absolute Deviation (MAD) tells you how spread out numbers are in a data set. The bigger the MAD, the more varied your numbers are. Simple as that.

In 7th grade math, you'll encounter MAD in statistics units. It's one of those concepts that looks confusing at first but falls apart once you see the steps.

Unlike standard deviation, MAD uses absolute values—so you ignore whether numbers are above or below the mean. You just care about how far off each value is.

The MAD Formula

Here's what you're working with:

MAD = (Σ|x - x̄|) / n

Where:

Don't let the symbols scare you. The calculation is straightforward arithmetic.

How to Calculate MAD: Step by Step

Let's walk through an example. Here's the data set:

Data: 4, 8, 6, 5, 3

Step 1: Find the Mean

Add everything up and divide by how many numbers you have.

4 + 8 + 6 + 5 + 3 = 26
26 ÷ 5 = 5.2

Step 2: Find Each Deviation

Subtract the mean from every number. Drop any negative sign.

Number (x) x - Mean |x - x̄|
4 4 - 5.2 = -1.2 1.2
8 8 - 5.2 = 2.8 2.8
6 6 - 5.2 = 0.8 0.8
5 5 - 5.2 = -0.2 0.2
3 3 - 5.2 = -2.2 2.2

Step 3: Add the Absolute Deviations

1.2 + 2.8 + 0.8 + 0.2 + 2.2 = 7.2

Step 4: Divide by the Count

7.2 ÷ 5 = 1.44

Answer: MAD = 1.44

This means, on average, each number in your data set sits 1.44 units away from the mean.

Practice Worksheet #1

Try these problems. Answers are at the bottom.

Problem 1: Find the MAD for {2, 4, 6, 8, 10}

Problem 2: Find the MAD for {12, 15, 18, 21, 24}

Problem 3: Find the MAD for {7, 7, 7, 7, 7}

Problem 4: A basketball player scored 14, 18, 22, 16, and 20 points in five games. What's their scoring MAD?

Problem 5: Class test scores: 85, 90, 78, 92, 88, 76, 95. Find the MAD.

Common Mistakes to Avoid

Comparing MAD to Other Spread Measures

Measure What It Tells You Difficulty
Range Distance between highest and lowest Easy
Mean Absolute Deviation Average distance from the mean Medium
Variance Average squared distance from the mean Hard
Standard Deviation Square root of variance Hardest

MAD is the most intuitive of the bunch. It literally tells you "on average, how far off is each value?"

Quick Reference: MAD Checklist

Answer Key

Problem 1: Mean = 6. Deviations: 4, 2, 0, 2, 4. Sum = 12. MAD = 12 ÷ 5 = 2.4

Problem 2: Mean = 18. Deviations: 6, 3, 0, 3, 6. Sum = 18. MAD = 18 ÷ 5 = 3.6

Problem 3: Mean = 7. All deviations = 0. MAD = 0 (no spread at all)

Problem 4: Mean = 18. Deviations: 4, 0, 4, 2, 2. Sum = 12. MAD = 12 ÷ 5 = 2.4

Problem 5: Mean = 86.29. Deviations: 1.29, 3.71, 8.29, 5.71, 1.71, 10.29, 8.71. Sum = 39.71. MAD = 39.71 ÷ 7 = 5.67

Why Teachers Love MAD Questions on Tests

State testing and end-of-year exams love MAD because it tests multiple skills at once:

Master MAD and you prove you can handle multi-step math. That's the real reason you're learning this.