Math worksheet for calculating mean absolute deviation with four data sets and structured tables.

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:

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 mean of these absolute differences.

Let's solve each data set step by step.

---

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

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

#### Step 2: Calculate the difference between each data point and the mean
\[
\begin{aligned}
&\text{Difference for } 12: 12 - 16 = -4 \\
&\text{Difference for } 19: 19 - 16 = 3 \\
&\text{Difference for } 10: 10 - 16 = -6 \\
&\text{Difference for } 18: 18 - 16 = 2 \\
&\text{Difference for } 21: 21 - 16 = 5 \\
\end{aligned}
\]

#### Step 3: Take the absolute value of each difference
\[
\begin{aligned}
&\text{Absolute value for } -4: | -4 | = 4 \\
&\text{Absolute value for } 3: | 3 | = 3 \\
&\text{Absolute value for } -6: | -6 | = 6 \\
&\text{Absolute value for } 2: | 2 | = 2 \\
&\text{Absolute value for } 5: | 5 | = 5 \\
\end{aligned}
\]

#### Step 4: Find the mean of these absolute differences
\[
\text{Mean Absolute Deviation} = \frac{\text{Sum of absolute differences}}{\text{Number of data points}}
\]
\[
\text{Sum of absolute differences} = 4 + 3 + 6 + 2 + 5 = 20
\]
\[
\text{Mean Absolute Deviation} = \frac{20}{5} = 4.00
\]

---

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

#### Step 1: Calculate the mean
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
\]
\[
\text{Mean} = \frac{7 + 14 + 11 + 13 + 4 + 20}{6} = \frac{79}{6} \approx 13.17
\]

#### Step 2: Calculate the difference between each data point and the mean
\[
\begin{aligned}
&\text{Difference for } 7: 7 - 13.17 = -6.17 \\
&\text{Difference for } 14: 14 - 13.17 = 0.83 \\
&\text{Difference for } 11: 11 - 13.17 = -2.17 \\
&\text{Difference for } 13: 13 - 13.17 = -0.17 \\
&\text{Difference for } 4: 4 - 13.17 = -9.17 \\
&\text{Difference for } 20: 20 - 13.17 = 6.83 \\
\end{aligned}
\]

#### Step 3: Take the absolute value of each difference
\[
\begin{aligned}
&\text{Absolute value for } -6.17: | -6.17 | = 6.17 \\
&\text{Absolute value for } 0.83: | 0.83 | = 0.83 \\
&\text{Absolute value for } -2.17: | -2.17 | = 2.17 \\
&\text{Absolute value for } -0.17: | -0.17 | = 0.17 \\
&\text{Absolute value for } -9.17: | -9.17 | = 9.17 \\
&\text{Absolute value for } 6.83: | 6.83 | = 6.83 \\
\end{aligned}
\]

#### Step 4: Find the mean of these absolute differences
\[
\text{Mean Absolute Deviation} = \frac{\text{Sum of absolute differences}}{\text{Number of data points}}
\]
\[
\text{Sum of absolute differences} = 6.17 + 0.83 + 2.17 + 0.17 + 9.17 + 6.83 = 25.34
\]
\[
\text{Mean Absolute Deviation} = \frac{25.34}{6} \approx 4.22
\]

---

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

#### Step 1: Calculate the mean
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
\]
\[
\text{Mean} = \frac{50 + 48 + 36 + 45 + 33 + 37}{6} = \frac{249}{6} = 41.5
\]

#### Step 2: Calculate the difference between each data point and the mean
\[
\begin{aligned}
&\text{Difference for } 50: 50 - 41.5 = 8.5 \\
&\text{Difference for } 48: 48 - 41.5 = 6.5 \\
&\text{Difference for } 36: 36 - 41.5 = -5.5 \\
&\text{Difference for } 45: 45 - 41.5 = 3.5 \\
&\text{Difference for } 33: 33 - 41.5 = -8.5 \\
&\text{Difference for } 37: 37 - 41.5 = -4.5 \\
\end{aligned}
\]

#### Step 3: Take the absolute value of each difference
\[
\begin{aligned}
&\text{Absolute value for } 8.5: | 8.5 | = 8.5 \\
&\text{Absolute value for } 6.5: | 6.5 | = 6.5 \\
&\text{Absolute value for } -5.5: | -5.5 | = 5.5 \\
&\text{Absolute value for } 3.5: | 3.5 | = 3.5 \\
&\text{Absolute value for } -8.5: | -8.5 | = 8.5 \\
&\text{Absolute value for } -4.5: | -4.5 | = 4.5 \\
\end{aligned}
\]

#### Step 4: Find the mean of these absolute differences
\[
\text{Mean Absolute Deviation} = \frac{\text{Sum of absolute differences}}{\text{Number of data points}}
\]
\[
\text{Sum of absolute differences} = 8.5 + 6.5 + 5.5 + 3.5 + 8.5 + 4.5 = 37.0
\]
\[
\text{Mean Absolute Deviation} = \frac{37.0}{6} \approx 6.17
\]

---

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

#### Step 1: Calculate the mean
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
\]
\[
\text{Mean} = \frac{8 + 5 + 2 + 9}{4} = \frac{24}{4} = 6
\]

#### Step 2: Calculate the difference between each data point and the mean
\[
\begin{aligned}
&\text{Difference for } 8: 8 - 6 = 2 \\
&\text{Difference for } 5: 5 - 6 = -1 \\
&\text{Difference for } 2: 2 - 6 = -4 \\
&\text{Difference for } 9: 9 - 6 = 3 \\
\end{aligned}
\]

#### Step 3: Take the absolute value of each difference
\[
\begin{aligned}
&\text{Absolute value for } 2: | 2 | = 2 \\
&\text{Absolute value for } -1: | -1 | = 1 \\
&\text{Absolute value for } -4: | -4 | = 4 \\
&\text{Absolute value for } 3: | 3 | = 3 \\
\end{aligned}
\]

#### Step 4: Find the mean of these absolute differences
\[
\text{Mean Absolute Deviation} = \frac{\text{Sum of absolute differences}}{\text{Number of data points}}
\]
\[
\text{Sum of absolute differences} = 2 + 1 + 4 + 3 = 10
\]
\[
\text{Mean Absolute Deviation} = \frac{10}{4} = 2.50
\]

---

Final Answers:

\[
\boxed{4.00, 4.22, 6.17, 2.50}
\]