Mean Absolute Deviation activity - Free Printable

Of course! Let's solve each problem step by step. The Mean Absolute Deviation (MAD) is a measure of how spread out the numbers in a data set are from the mean (average). Here’s how to calculate it:

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✔ Steps to Find Mean Absolute Deviation:

1. Find the mean of the data set.
2. Find the difference between each data point and the mean.
3. Take the absolute value of each difference (ignore negative signs).
4. Find the mean of those absolute differences.

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## 🔢 Problem 1: Data Set = 26, 25, 30, 40, 50, 65

Step 1: Find the Mean

Add all numbers:
26 + 25 + 30 + 40 + 50 + 65 = 236
Number of data points = 6
→ Mean = 236 ÷ 6 = 39.333... (We’ll use 39.33 for calculation)

Step 2 & 3: Fill the Table

| Data | Mean | Difference (Data - Mean) | Absolute |
|------|--------|--------------------------|----------|
| 26 | 39.33 | 26 - 39.33 = -13.33 | 13.33 |
| 25 | 39.33 | 25 - 39.33 = -14.33 | 14.33 |
| 30 | 39.33 | 30 - 39.33 = -9.33 | 9.33 |
| 40 | 39.33 | 40 - 39.33 = 0.67 | 0.67 |
| 50 | 39.33 | 50 - 39.33 = 10.67 | 10.67 |
| 65 | 39.33 | 65 - 39.33 = 25.67 | 25.67 |
| | | Sum of Absolute | 74.00|

Step 4: Find MAD

MAD = Sum of Absolute Differences ÷ Number of Data Points
→ 74.00 ÷ 6 ≈ 12.33

✔ Mean Absolute Deviation = 12.33

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## 🔢 Problem 2: Data Set = 80, 75, 35, 56, 78, 90, 40

Step 1: Find the Mean

Sum = 80 + 75 + 35 + 56 + 78 + 90 + 40 = 354
Number of data points = 7
→ Mean = 354 ÷ 7 ≈ 50.57

Step 2 & 3: Fill the Table

| Data | Mean | Difference | Absolute |
|------|--------|--------------------|----------|
| 80 | 50.57 | 80 - 50.57 = 29.43 | 29.43 |
| 75 | 50.57 | 75 - 50.57 = 24.43 | 24.43 |
| 35 | 50.57 | 35 - 50.57 = -15.57| 15.57 |
| 56 | 50.57 | 56 - 50.57 = 5.43 | 5.43 |
| 78 | 50.57 | 78 - 50.57 = 27.43 | 27.43 |
| 90 | 50.57 | 90 - 50.57 = 39.43 | 39.43 |
| 40 | 50.57 | 40 - 50.57 = -10.57| 10.57 |
| | | Sum of Absolute| 152.29|

Step 4: Find MAD

MAD = 152.29 ÷ 7 ≈ 21.76

✔ Mean Absolute Deviation = 21.76

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## 🔢 Problem 3: Data Set = 24, 45, 50, 30, 65, 80

Step 1: Find the Mean

Sum = 24 + 45 + 50 + 30 + 65 + 80 = 294
Number of data points = 6
→ Mean = 294 ÷ 6 = 49

Step 2 & 3: Fill the Table

| Data | Mean | Difference | Absolute |
|------|------|-----------------|----------|
| 24 | 49 | 24 - 49 = -25 | 25 |
| 45 | 49 | 45 - 49 = -4 | 4 |
| 50 | 49 | 50 - 49 = 1 | 1 |
| 30 | 49 | 30 - 49 = -19 | 19 |
| 65 | 49 | 65 - 49 = 16 | 16 |
| 80 | 49 | 80 - 49 = 31 | 31 |
| | | Sum of Absolute | 96 |

Step 4: Find MAD

MAD = 96 ÷ 6 = 16

✔ Mean Absolute Deviation = 16

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## 🔢 Problem 4: Data Set = 10, 9, 7, 15, 6, 7, 3

Step 1: Find the Mean

Sum = 10 + 9 + 7 + 15 + 6 + 7 + 3 = 47
Number of data points = 7
→ Mean = 47 ÷ 7 ≈ 6.71

Step 2 & 3: Fill the Table

| Data | Mean | Difference | Absolute |
|------|--------|-----------------|----------|
| 10 | 6.71 | 10 - 6.71 = 3.29| 3.29 |
| 9 | 6.71 | 9 - 6.71 = 2.29 | 2.29 |
| 7 | 6.71 | 7 - 6.71 = 0.29 | 0.29 |
| 15 | 6.71 | 15 - 6.71 = 8.29| 8.29 |
| 6 | 6.71 | 6 - 6.71 = -0.71| 0.71 |
| 7 | 6.71 | 7 - 6.71 = 0.29 | 0.29 |
| 3 | 6.71 | 3 - 6.71 = -3.71| 3.71 |
| | | Sum of Absolute | 18.87 |

Step 4: Find MAD

MAD = 18.87 ÷ 7 ≈ 2.696 → Round to 2.70

✔ Mean Absolute Deviation = 2.70

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## 📝 Final Answers:

1. Mean Absolute Deviation = 12.33
2. Mean Absolute Deviation = 21.76
3. Mean Absolute Deviation = 16
4. Mean Absolute Deviation = 2.70

You can now fill in your worksheet with these values!

Let me know if you’d like to see this in a printable table format or need help rounding differently. 😊