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).