The following table shows the number of classes that each teacher in the math department at Wilburton High School teaches.

TeacherMr. LinnMrs. RossMr. RileyMs. Moss

**Number of classes**

\[3\]

\[7\]

\[4\]

\[2\]

**Find the mean absolute deviation (MAD) of the data set.**

 classes

To find the Mean Absolute Deviation (MAD) of the data set, follow these steps:

### 1. Calculate the Mean (Average) Number of Classes
First, find the mean (average) of the number of classes:

\[
\text{Mean} = \frac{3 + 7 + 4 + 2}{4} = \frac{16}{4} = 4
\]

### 2. Find the Absolute Deviations from the Mean
Next, find the absolute deviation of each teacher's number of classes from the mean:

- Mr. Linn: \(|3 - 4| = 1\)
- Mrs. Ross: \(|7 - 4| = 3\)
- Mr. Riley: \(|4 - 4| = 0\)
- Ms. Moss: \(|2 - 4| = 2\)

### 3. Calculate the Mean of the Absolute Deviations
Finally, calculate the mean of these absolute deviations:

\[
\text{MAD} = \frac{1 + 3 + 0 + 2}{4} = \frac{6}{4} = 1.5
\]

So, the Mean Absolute Deviation (MAD) of the data set is **1.5 classes**.

Would you like more details on how this was calculated, or do you have any questions?

Here are 8 questions that expand on this information:
1. What is the significance of the Mean Absolute Deviation in a data set?
2. How would the MAD change if one teacher taught 10 classes instead of 7?
3. Can the MAD ever be zero? If so, under what circumstances?
4. How does MAD differ from standard deviation?
5. What are some real-world applications of using MAD?
6. How would the MAD change if there were more teachers with the same number of classes?
7. What does a higher MAD indicate about the variability of the data set?
8. How would the MAD calculation change if we had 10 teachers?

**Tip:** The MAD is a measure of variability that gives you an idea of how spread out the data is around the mean, without being affected by outliers as much as standard deviation.

Learn how to calculate the Mean Absolute Deviation (MAD) for the number of classes taught by teachers at Wilburton High School. Follow a step-by-step solution to find the MAD, which measures the average deviation of each teacher's class load from the mean number of classes. Suitable for high school students studying statistics.

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