Student Handout with Possible Answers Topic: Comparing Groups Lesson 3: Activity 1

**Interpreting Boxplots**[1]

Part I

The following graph shows the distribution of ages for 72 recent Academy Award winners split up by gender (36 females and 36 males).

*Use the graph to help answer the following questions.*

a) Estimate the percentage of female Oscar winners who are younger than 40.

*About 70% since the third quartile is at about 42.*

b) The oldest 50% of Oscar winners who are male are between which two ages?

*They are (approximately) between 37 and 49 years old.*

c) What is the shape of the distribution of male Oscar winners? Explain.

*The distribution of male Oscar winners is right skewed because the whisker representing the fourth quarter of winners is longer than the whisker representing the first fourth. There is also an outlier: a 76 year-old male Oscar winner.*

d) Explain how to find the Inter-Quartile Range (IQR) for the female Oscar winners.

*The IQR is the difference between the value of the third quartile (Q 3) and the first quartile (Q 1). For female Oscar winners, Q 3 = 42 and Q 1 = 30. We would subtract the value of Q 1 from the value of Q 3.*

*Therefore, the IQR for female Oscar winners is Q 3 – Q 1 = 42 – 30 = 12.*

e) Find the IQR for the female Oscar winners.

*The IQR for female Oscar winners is Q 3 – Q 1 = 42 – 30 = 12.*

f) What information does the IQR of the female Oscar winners offer us? Why would a statistician be more interested in the IQR than in the range?

*The IQR of the female Oscar winners tells us that the middle 50% of women who win Oscars are within 12 years of one another. A statistician may be more interested in the IQR because she may be more interested in knowing about the variability of the middle 50% of the data.*

g) Compare the medians for male and female Oscar winners. What do you conclude about the ages of male and female Oscar winners? Explain.

*The median ages for male and female Oscar winners are 43 and 35 respectively. Based on knowledge about medians alone, we can say that Oscar winners who are female tend to be younger.*

h) Compare the IQR for the male and female Oscar winners. What do you conclude about the ages of male and female Oscar winners now? Explain.

*From part e) above, the IQR for female Oscar winners is 12. From part b) above, we can deduce that the IQR for male Oscar winners is 49 – 37 = 12.*

*This reinforces my conclusion in part g) above that Oscar winners who are female tend to be younger because both male and female Oscar winners have the same spread of ages in the middle 50% whereas the median age for male Oscar winners is 8 years older than the median age for female Oscar winners.*

Part II

In the next problem, you will be given a descriptive scenario and a graph that shows two box plots. Use the graphs to make an informed comparison of the groups.

§ Be sure to compare shape, center and spread of the distributions.

§ Also, be sure that you are comparing the groups using the context of the data and not just comparing two (or more) numbers.

Stephen wants to investigate differences in spending habits of males and females. He compares the amounts spent per week on reading materials by males and females in a random sample of college students by generating the following plots.

Help Stephen by comparing the two distributions.

*The median cost of spending on reading materials by males and females are 3.2 and 2 respectively, while their spread as measured by the interquartile range (IQR) is the same: reading costs are 5 per week.*

*The distribution of female reading costs is more positively skewed than the distribution of male reading costs but has a shorter tail. For both males and females, 25% or more students reported that they did not have reading costs. However, 50% of the female students have two or less reading costs per week compared to 50% of the male who reported having three or less reading costs per week.*

*Overall, we can say that the range of spending costs per week for reading for male students is wider, 10 as opposed to 7 for female students. Even though the same percent of male and female students did not have any reading costs and the middle 50% of male and students have 0 to 5 reading costs per week, 25% of males have between 3 and 5 reading costs per week whereas there are fewer than 25% of females who have the same costs. Also, 25% of males have between 5 to 10 reading costs while 25% of females have between 5 and 7 reading costs per week.*

*In conclusion, male spending is more varied and the amount tended to be more than female spending on reading costs per week (less varied and the amount tended to be less). *

Reference

Garfield, J., Zieffler, A., & Lane-Getaz, S. (2005). EPSY 3264 Course Packet, University of Minnesota, Minneapolis, MN.

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[1] Please note the possible student answers may not, in some cases, be IDEAL student answers.