If a data set included the numbers 13, 14, 14, 16, 16, 16, 16, 18, 18, 19 what would the mean absolute deviation be?

To find the **mean absolute deviation (MAD)** of a data set, we follow these steps:

1. **Calculate the mean** of the data set.
2. **Find the absolute deviations** of each value from the mean.
3. **Calculate the mean** of these absolute deviations.

Let's go through each step.

### Step 1: Calculate the Mean
The numbers in the data set are:  
13, 14, 14, 16, 16, 16, 16, 18, 18, 19

The mean is:
\[
\text{Mean} = \frac{13 + 14 + 14 + 16 + 16 + 16 + 16 + 18 + 18 + 19}{10} = \frac{160}{10} = 16
\]

### Step 2: Find the Absolute Deviations from the Mean
Now, we calculate the absolute deviation of each number from the mean of 16:

- |13 - 16| = 3
- |14 - 16| = 2
- |14 - 16| = 2
- |16 - 16| = 0
- |16 - 16| = 0
- |16 - 16| = 0
- |16 - 16| = 0
- |18 - 16| = 2
- |18 - 16| = 2
- |19 - 16| = 3

### Step 3: Calculate the Mean of the Absolute Deviations
Now, add these deviations and divide by the number of values:

\[
\text{MAD} = \frac{3 + 2 + 2 + 0 + 0 + 0 + 0 + 2 + 2 + 3}{10} = \frac{14}{10} = 1.4
\]

### Answer
The **mean absolute deviation** of the data set is:
\[
\text{MAD} = 1.4
\]

Would you like further details on this process or have any additional questions?

Here are some related questions:
1. How is the mean affected by outliers in a data set?
2. What are other ways to measure variability in data?
3. How does MAD compare to standard deviation?
4. Can MAD be used with non-numeric data, such as ordinal data?
5. How does changing one value in the data set impact the MAD?

**Tip:** MAD is a robust measure of variability because it’s less sensitive to outliers than standard deviation.

Learn how to calculate the mean absolute deviation (MAD) of the data set {13, 14, 14, 16, 16, 16, 16, 18, 18, 19}. This step-by-step guide covers finding the mean, calculating absolute deviations, and determining the final MAD value. Perfect for students in Grades 6-8 studying basic statistics.

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