Let's calculate the mean absolute deviation (MAD) for the given data set:
The data points are:
$10, 20, 12, 4, 18, 8, 14, 18$

Step 1: Find the mean of the data set. $\text{Mean} = \frac{10 + 20 + 12 + 4 + 18 + 8 + 14 + 18}{8} = \frac{104}{8} = 13$

Step 2: Find the absolute deviations from the mean for each data point.

• |10 - 13| = 3
• |20 - 13| = 7
• |12 - 13| = 1
• |4 - 13| = 9
• |18 - 13| = 5
• |8 - 13| = 5
• |14 - 13| = 1
• |18 - 13| = 5

Step 3: Find the mean of these absolute deviations. $\text{MAD} = \frac{3 + 7 + 1 + 9 + 5 + 5 + 1 + 5}{8} = \frac{36}{8} = 4.5$

Thus, the mean absolute deviation is 4.5.

The value shown in the image (8) seems incorrect. Would you like any additional details or have any questions?

Here are 5 related questions:

1. How does mean absolute deviation differ from standard deviation?
2. What is the significance of absolute deviations?
3. How is mean absolute deviation used in real-world data analysis?
4. Can you calculate the standard deviation for the same data set?
5. How would removing or adding a value affect the MAD?

Tip: The mean absolute deviation helps in understanding how spread out the data points are from the mean, giving a simple measure of variability!