Measures of Central Tendency for Numerical Data Practice Questions

To review these concepts, go to Measures of Central Tendency for Numerical Data Study Guide.

Measures of Central Tendency for Numerical Data Practice Questions

Practice

From 1996 to 2004, the ages of the best actors at the time of winning the award were 45, 59, 45, 42, 35, 46, 28, 42, and 36. The ages of the best actresses at the time of winning the award for this same time period were 39, 33, 25, 24, 32, 32, 34, 27, and 30.

1. These are two populations, one for best actors and one for best actresses. Why are these populations and not samples?
2. Find the mean age of women winning the Oscar for best actress from 1996 to 2004.
3. Find the median age of men winning the Oscar for best actor from 1996 to 2004.
4. Find the median age of women winning the Oscar for best actress from 1996 to 2004.
5. Is the mode a useful measure of central tendency for either population? Explain.
6. Which of the measures of central tendency provides the best measure of the middle of these two population distributions? Explain.
7. Using the population parameters in the first five practice problems, discuss how the centers of these distributions compare.

Previously, we created a dotplot and a stem-and-leaf plot for the average hours of sleep for 20 high school students who had been randomly selected from a very large high school (Dotplots and Stem-and-Leaf Plots Practice Problems). They had kept a record of the number of hours they slept each night for a week. These seven values were averaged to obtain an average night of sleep for each. The results were as follows: 9, 8, 8, 7.5, 6, 6, 4, 5.5, 7, 8, 5, 7.5, 6.5, 10, 8.5, 6.5, 5, 5.5, 7, and 7.5 hours.

8. These 20 data values represent a sample, not a population. What is the population from which they were drawn?
9. Find the sample mean.
10. Find the sample median.
11. Is the mode a useful measure of central tendency for these data?
12. Which of the measures of central tendency provides the best measure of center for these data? Explain.

Solutions

1. All ages for actors and actresses who won an Oscar from 1997 to 2004 are included in the set of ages, not just some of the ages.
2. 30.7
3. 42
4. 32
5. Yes. There are two modes for the actors' ages: 42 and 45, which are two ages in the middle of the data set and close to the mean. The mode for the actress' ages is 32, which is exactly in the middle of the data set and close to the mean.
6. The median provides the best measure of central tendency because there are two outliers for the actors' ages.
7. The centers of distribution for the actors' ages were higher than for the actress' centers, showing that the actors were generally older than the actresses at the time they received their awards.
8. All students at the very large high school.
9. 6.9 hours
10. 7 hours
11. No. There are two modes: 7.5 and 8, both of which are slightly higher than the middle of the data set.
12. The mean would provide the best measure of center because the units of data are close in value with no outliers, but the median would also work well in this case.