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Let's solve this step-by-step to find the **Mean Absolute Deviation (MAD)** for the given data set: **14, 10, 9, 12, 21, 14, 18**.

### Steps:
1. **Find the mean of the data set**:
   \[
   \text{Mean} = \frac{14 + 10 + 9 + 12 + 21 + 14 + 18}{7} = \frac{98}{7} = 14
   \]
   The mean is **14**.

2. **Find the absolute deviation from the mean** for each value:
   - \( |14 - 14| = 0 \)
   - \( |10 - 14| = 4 \)
   - \( |9 - 14| = 5 \)
   - \( |12 - 14| = 2 \)
   - \( |21 - 14| = 7 \)
   - \( |14 - 14| = 0 \)
   - \( |18 - 14| = 4 \)

   The absolute deviations are: **0, 4, 5, 2, 7, 0, 4**.

3. **Find the mean of the absolute deviations**:
   \[
   \text{MAD} = \frac{0 + 4 + 5 + 2 + 7 + 0 + 4}{7} = \frac{22}{7} \approx 3.14
   \]

So, the **Mean Absolute Deviation** is approximately **3.14**.

Would you like further details or have any questions? Here are some related questions for better understanding:

1. What is the significance of the mean absolute deviation in data analysis?
2. How is MAD different from standard deviation?
3. How does rounding affect the precision of your results?
4. Can MAD be used for both small and large data sets? Why or why not?
5. How can you use MAD to compare variability between different data sets?

**Tip**: MAD is a robust measure of variability because it is not influenced by extreme values (outliers).

Find the mean absolute deviation for the data set: 14, 10, 9, 12, 21, 14, 18. Round your answer to the nearest hundredth.

Learn how to find the Mean Absolute Deviation (MAD) for the data set: 14, 10, 9, 12, 21, 14, 18. This step-by-step guide shows how to calculate the mean and absolute deviations and round the final MAD value to the nearest hundredth.

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