The data set below has 6 values.
Find the mean absolute deviation for the data set.
If necessary, round your answer to the nearest hundredth.
10, 8, 13, 19,8, 20

To find the **mean absolute deviation (MAD)** of the dataset, follow these steps:

1. **Find the mean (average) of the dataset:**
   \[
   \text{Mean} = \frac{10 + 8 + 13 + 19 + 8 + 20}{6} = \frac{78}{6} = 13
   \]

2. **Find the absolute deviations** from the mean for each data point:
   - \( |10 - 13| = 3 \)
   - \( |8 - 13| = 5 \)
   - \( |13 - 13| = 0 \)
   - \( |19 - 13| = 6 \)
   - \( |8 - 13| = 5 \)
   - \( |20 - 13| = 7 \)

3. **Calculate the mean of these absolute deviations:**
   \[
   \text{MAD} = \frac{3 + 5 + 0 + 6 + 5 + 7}{6} = \frac{26}{6} \approx 4.33
   \]

The **mean absolute deviation** is approximately **4.33**.

Would you like more details on the steps or have any other questions?

Here are five related questions to deepen your understanding:
1. How is the mean absolute deviation different from standard deviation?
2. What is the significance of absolute deviation in data analysis?
3. How would the MAD change if one value in the dataset were much larger or smaller?
4. What are other ways to measure variability in a dataset besides MAD?
5. Can MAD be zero? Under what circumstances?

**Tip:** The mean absolute deviation is a useful way to measure the spread of data, especially when you want to avoid squaring deviations as in variance or standard deviation.

Find the mean absolute deviation for the data set: 10, 8, 13, 19, 8, 20. Round your answer to the nearest hundredth if necessary.

Learn how to find the mean absolute deviation (MAD) for a data set with values 10, 8, 13, 19, 8, and 20. This tutorial includes step-by-step calculations to determine the mean, absolute deviations, and the MAD, rounded to the nearest hundredth. Ideal for middle school students in Grades 6-8.

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