Measures of Variation

Measures of Variation

Read each question carefully and answer to the best of your ability. Show all your work where necessary.

1. What is the range of a data set? Explain in your own words.

2. Find the range of the following data set: 12, 15, 9, 20, 18, 10.

3. The interquartile range (IQR) is the difference between the   quartile and the   quartile.

4. For the data set: 5, 8, 10, 12, 15, 18, 20, the median is  .

5. Using the same data set (5, 8, 10, 12, 15, 18, 20), the first quartile (Q1) is   and the third quartile (Q3) is  .

6. Calculate the IQR for the data set: 5, 8, 10, 12, 15, 18, 20. The IQR is  .

7. Which measure of variation describes the average distance between each data point and the mean?

8. A data set has a mean of 10. The absolute deviations from the mean are 2, 3, 1, 4. What is the Mean Absolute Deviation (MAD)?

9. Calculate the Mean Absolute Deviation (MAD) for the following data set: 8, 10, 12, 14, 16. Show your steps.

Step 1: Find the mean.

Step 2: Find the absolute deviation of each data point from the mean.

Step 3: Find the mean of these absolute deviations.

10. A larger range always means that the data points are more spread out.

11. The IQR is less affected by outliers than the range.