3. Describing Data Numerically

Using Technology to Find Quartiles and Draw Graphs In Exercises 23–26, use technology to draw a box-and-whisker plot that represents the data set.

Vacation Days The number of vacation days used by a sample of 20 employees in a recent year

3 9 2 1 7 5 3 2 2 6

4 0 10 0 3 5 7 8 6 5

Studying Refer to the data set in Exercise 23 and the box-and-whisker plot you drew that represents the data set.

c. You randomly select one student from the sample. What is the likelihood that the student studied less than 2 hours per day? Write your answer as a percent.

Drawing a Box-and-Whisker Plot In Exercises 15–18,

(b) draw a box-and-whisker plot that represents the data set.

39 36 30 27 26 24 28 35 39 60 50 41 35 32 51

Drawing a Box-and-Whisker Plot In Exercises 15–18,

(b) draw a box-and-whisker plot that represents the data set.

171 176 182 150 178 180 173 170 174 178 181 180

Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown.

a. Describe the shape of each distribution. Which concert has less variation in song lengths?

Song Lengths Side-by-side box-and-whisker plots can be used to compare two or more different data sets. Each box-and-whisker plot is drawn on the same number line to compare the data sets more easily. The lengths (in seconds) of songs played at two different concerts are shown.

d. Can you determine which concert lasted longer? Explain.

Modified Box-and-Whisker Plot In Exercises 59–62, (a) identify any outliers and (b) draw a modified box-and-whisker plot that represents the data set. Use asterisks (*) to identify outliers.

75 78 80 75 62 72 74 75 80 95 76 72

You are a member of your local apartment association. The association represents rental housing owners and managers who operate residential rental property throughout the greater metropolitan area. Recently, the association has received several complaints from tenants in a particular area of the city who feel that their monthly rental fees are much higher compared to other parts of the city.

You want to investigate the rental fees. You gather the data shown in the table at the right. Area A represents the area of the city where tenants are unhappy about their monthly rents. The data represent the monthly rents paid by a random sample of tenants in Area A and three other areas of similar size. Assume all the apartments represented are approximately the same size with the same amenities.

c. Based on your data displays, does it appear that the monthly rents in Area A are higher than the rents in the other areas of the city? Explain.

Graphical Analysis In Exercises 13 and 14, use the box-and-whisker plot to identify the five-number summary.

Drawing a Box-and-Whisker Plot In Exercises 15–18,

(a) find the five-number summary

4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9

"[DATA] Fumbles The New England Patriots made headlines prior to the 2015 Super Bowl for allegedly playing with underinflated footballs. An underinflated ball is easier to grip, and therefore, less likely to be fumbled. What do the data say? The following data represent the number of plays a team has per fumble. For example, the Chicago Bears run 48 offensive plays for every fumble.

a. Draw a boxplot of plays per fumble for all teams in the National Football League. Describe the shape of the distribution. Are there any outliers? If so, which team(s)?"

[DATA] Tax Rates Do women feel differently from men when it comes to federal tax rates? One question on the Sullivan Statistics Survey II was, “What percent of income do you believe individuals should pay in federal income tax?” Results of the survey may be found at www.pearsonhighered.com/sullivanstats. Select the data file SullivanSurveyII using the file format of your choice for the version of the text you are using. The Tax Rate column contains the response.

a. Draw side-by-side boxplots of tax rates by gender. Does there appear to be a difference in the tax rates for the genders?

[DATA] Bull and Bear Markets The stock market goes through periods known as bull markets and bear markets. A bull market exists when the stock market increases in value by at least 20%, while a bear market exists when the stock market decreases in value by at least 20%. The data below represent the number of months a random sample of bull and bear markets have lasted.

d. Draw a side-by-side boxplot by market condition. Discuss any interesting features of the graph.