Mean Absolute Deviation Worksheets - Free Printable

To solve the problem of finding the Mean Absolute Deviation (MAD) for each data set, we need to follow these steps:

Steps to Calculate Mean Absolute Deviation (MAD):

1. Find the Mean of the data set.
2. Calculate the Difference between each data point and the mean.
3. Take the Absolute Value of each difference.
4. Find the Sum of all absolute values.
5. Divide the Sum by the number of data points to get the MAD.

Let's solve each part step by step.

---

1) Data Set: 12, 19, 10, 18, 21

#### Step 1: Find the Mean
The mean is calculated as:
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
\]
\[
\text{Mean} = \frac{12 + 19 + 10 + 18 + 21}{5} = \frac{80}{5} = 16
\]

#### Step 2: Calculate the Differences
For each data point, subtract the mean:
- For 12: \( 12 - 16 = -4 \)
- For 19: \( 19 - 16 = 3 \)
- For 10: \( 10 - 16 = -6 \)
- For 18: \( 18 - 16 = 2 \)
- For 21: \( 21 - 16 = 5 \)

#### Step 3: Take the Absolute Values
- \( | -4 | = 4 \)
- \( | 3 | = 3 \)
- \( | -6 | = 6 \)
- \( | 2 | = 2 \)
- \( | 5 | = 5 \)

#### Step 4: Find the Sum of Absolute Values
\[
\text{Sum} = 4 + 3 + 6 + 2 + 5 = 20
\]

#### Step 5: Calculate the MAD
\[
\text{MAD} = \frac{\text{Sum of Absolute Values}}{\text{Number of data points}} = \frac{20}{5} = 4
\]

So, the Mean Absolute Deviation for the first data set is:
\[
\boxed{4}
\]

---

2) Data Set: 7, 14, 11, 13, 4, 20

#### Step 1: Find the Mean
\[
\text{Mean} = \frac{7 + 14 + 11 + 13 + 4 + 20}{6} = \frac{79}{6} \approx 13.17
\]

#### Step 2: Calculate the Differences
- For 7: \( 7 - 13.17 = -6.17 \)
- For 14: \( 14 - 13.17 = 0.83 \)
- For 11: \( 11 - 13.17 = -2.17 \)
- For 13: \( 13 - 13.17 = -0.17 \)
- For 4: \( 4 - 13.17 = -9.17 \)
- For 20: \( 20 - 13.17 = 6.83 \)

#### Step 3: Take the Absolute Values
- \( | -6.17 | = 6.17 \)
- \( | 0.83 | = 0.83 \)
- \( | -2.17 | = 2.17 \)
- \( | -0.17 | = 0.17 \)
- \( | -9.17 | = 9.17 \)
- \( | 6.83 | = 6.83 \)

#### Step 4: Find the Sum of Absolute Values
\[
\text{Sum} = 6.17 + 0.83 + 2.17 + 0.17 + 9.17 + 6.83 = 25.34
\]

#### Step 5: Calculate the MAD
\[
\text{MAD} = \frac{\text{Sum of Absolute Values}}{\text{Number of data points}} = \frac{25.34}{6} \approx 4.22
\]

So, the Mean Absolute Deviation for the second data set is:
\[
\boxed{4.22}
\]

---

3) Data Set: 50, 48, 36, 45, 33, 37

#### Step 1: Find the Mean
\[
\text{Mean} = \frac{50 + 48 + 36 + 45 + 33 + 37}{6} = \frac{249}{6} = 41.5
\]

#### Step 2: Calculate the Differences
- For 50: \( 50 - 41.5 = 8.5 \)
- For 48: \( 48 - 41.5 = 6.5 \)
- For 36: \( 36 - 41.5 = -5.5 \)
- For 45: \( 45 - 41.5 = 3.5 \)
- For 33: \( 33 - 41.5 = -8.5 \)
- For 37: \( 37 - 41.5 = -4.5 \)

#### Step 3: Take the Absolute Values
- \( | 8.5 | = 8.5 \)
- \( | 6.5 | = 6.5 \)
- \( | -5.5 | = 5.5 \)
- \( | 3.5 | = 3.5 \)
- \( | -8.5 | = 8.5 \)
- \( | -4.5 | = 4.5 \)

#### Step 4: Find the Sum of Absolute Values
\[
\text{Sum} = 8.5 + 6.5 + 5.5 + 3.5 + 8.5 + 4.5 = 37
\]

#### Step 5: Calculate the MAD
\[
\text{MAD} = \frac{\text{Sum of Absolute Values}}{\text{Number of data points}} = \frac{37}{6} \approx 6.17
\]

So, the Mean Absolute Deviation for the third data set is:
\[
\boxed{6.17}
\]

---

4) Data Set: 8, 5, 2, 9

#### Step 1: Find the Mean
\[
\text{Mean} = \frac{8 + 5 + 2 + 9}{4} = \frac{24}{4} = 6
\]

#### Step 2: Calculate the Differences
- For 8: \( 8 - 6 = 2 \)
- For 5: \( 5 - 6 = -1 \)
- For 2: \( 2 - 6 = -4 \)
- For 9: \( 9 - 6 = 3 \)

#### Step 3: Take the Absolute Values
- \( | 2 | = 2 \)
- \( | -1 | = 1 \)
- \( | -4 | = 4 \)
- \( | 3 | = 3 \)

#### Step 4: Find the Sum of Absolute Values
\[
\text{Sum} = 2 + 1 + 4 + 3 = 10
\]

#### Step 5: Calculate the MAD
\[
\text{MAD} = \frac{\text{Sum of Absolute Values}}{\text{Number of data points}} = \frac{10}{4} = 2.5
\]

So, the Mean Absolute Deviation for the fourth data set is:
\[
\boxed{2.5}
\]

---

Final Answers:

1. \( \boxed{4} \)
2. \( \boxed{4.22} \)
3. \( \boxed{6.17} \)
4. \( \boxed{2.5} \)