Worksheet for calculating mean absolute deviation with four practice problems and example data sets.

Problem Description:

The task involves calculating the Mean Absolute Deviation (MAD) for two sets of data. The Mean Absolute Deviation is a measure of variability in a dataset, calculated as the average of the absolute differences between each data point and the mean of the dataset.

#### Formula for Mean Absolute Deviation (MAD):
\[
\text{MAD} = \frac{\sum_{i=1}^{n} |x_i - \bar{x}|}{n}
\]
Where:
- \( x_i \) is each data point in the dataset.
- \( \bar{x} \) is the mean of the dataset.
- \( n \) is the number of data points.

Step-by-Step Solution:

#### Part 1: Calculate MAD for the first dataset
The first dataset is: 30, 40, 50, 60, 70

1. Calculate the mean (\( \bar{x} \)):
\[
\bar{x} = \frac{30 + 40 + 50 + 60 + 70}{5} = \frac{250}{5} = 50
\]

2. Calculate the absolute deviations from the mean:
- For \( x_1 = 30 \): \( |30 - 50| = 20 \)
- For \( x_2 = 40 \): \( |40 - 50| = 10 \)
- For \( x_3 = 50 \): \( |50 - 50| = 0 \)
- For \( x_4 = 60 \): \( |60 - 50| = 10 \)
- For \( x_5 = 70 \): \( |70 - 50| = 20 \)

3. Sum the absolute deviations:
\[
\sum |x_i - \bar{x}| = 20 + 10 + 0 + 10 + 20 = 60
\]

4. Calculate the MAD:
\[
\text{MAD} = \frac{\sum |x_i - \bar{x}|}{n} = \frac{60}{5} = 12
\]

So, the Mean Absolute Deviation for the first dataset is:
\[
\boxed{12}
\]

---

#### Part 2: Calculate MAD for the second dataset
The second dataset is: 28, 32, 35, 38, 40

1. Calculate the mean (\( \bar{x} \)):
\[
\bar{x} = \frac{28 + 32 + 35 + 38 + 40}{5} = \frac{173}{5} = 34.6
\]

2. Calculate the absolute deviations from the mean:
- For \( x_1 = 28 \): \( |28 - 34.6| = 6.6 \)
- For \( x_2 = 32 \): \( |32 - 34.6| = 2.6 \)
- For \( x_3 = 35 \): \( |35 - 34.6| = 0.4 \)
- For \( x_4 = 38 \): \( |38 - 34.6| = 3.4 \)
- For \( x_5 = 40 \): \( |40 - 34.6| = 5.4 \)

3. Sum the absolute deviations:
\[
\sum |x_i - \bar{x}| = 6.6 + 2.6 + 0.4 + 3.4 + 5.4 = 18.4
\]

4. Calculate the MAD:
\[
\text{MAD} = \frac{\sum |x_i - \bar{x}|}{n} = \frac{18.4}{5} = 3.68
\]

So, the Mean Absolute Deviation for the second dataset is:
\[
\boxed{3.68}
\]

---

Final Answers:

1. For the first dataset (30, 40, 50, 60, 70): \(\boxed{12}\)
2. For the second dataset (28, 32, 35, 38, 40): \(\boxed{3.68}\)