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To calculate the mean absolute deviation (MAD) of the given data set, follow these steps:

1. **Find the mean (average) of the data set:**
\[ \text{Data set: } 14, 14, 6, 6, 10, 10, 2, 18 \]

\[ \text{Mean} = \frac{14 + 14 + 6 + 6 + 10 + 10 + 2 + 18}{8} \]

\[ \text{Mean} = \frac{80}{8} = 10 \]

2. **Find the absolute deviation of each data point from the mean:**

\[ |14 - 10| = 4 \]
\[ |14 - 10| = 4 \]
\[ |6 - 10| = 4 \]
\[ |6 - 10| = 4 \]
\[ |10 - 10| = 0 \]
\[ |10 - 10| = 0 \]
\[ |2 - 10| = 8 \]
\[ |18 - 10| = 8 \]

3. **Find the mean of these absolute deviations:**

\[ \text{Sum of absolute deviations} = 4 + 4 + 4 + 4 + 0 + 0 + 8 + 8 = 32 \]

\[ \text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}} \]

\[ \text{MAD} = \frac{32}{8} = 4 \]

So, the mean absolute deviation of the given data set is **4**.

Would you like more details or have any questions?

Here are 5 related questions to further explore this topic:

1. How does the mean absolute deviation compare to the standard deviation for the same data set?
2. What is the impact of an outlier on the mean absolute deviation?
3. How is the mean absolute deviation used in real-world applications?
4. Can you calculate the variance for the same data set?
5. What is the difference between mean absolute deviation and median absolute deviation?

**Tip:** When comparing the spread of different data sets, the mean absolute deviation provides a simple measure of variability that is less sensitive to outliers than standard deviation.

What is the mean absolute deviation of the following set of data? 14, 14, 6, 6, 10, 10, 2, 18

Learn how to calculate the mean absolute deviation (MAD) for the data set {14, 14, 6, 6, 10, 10, 2, 18}. This solution includes finding the mean, calculating the absolute deviations, and deriving the final MAD. Suitable for Grades 6-8.

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