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.