Exam 2: Graphical Methods for Describing Data Distributions

When using histograms to compare groups of different sizes, one may use either frequencies or relative frequencies for the vertical axis and still be effective.

A segmented bar chart uses rectangles rather than circles to display different categories in a set of data.

One of the "media messages" sent by television is that appearance is very important. These messages are thought to spur young women to have unrealistic expectations about beauty, thus encouraging women to spend more money on cosmetics and toiletries. During a recent prime-time television season investigators kept track of "appearance" comments. Data on comments by TV males, classified by gender of the comment recipient and type of appearance comment, are given in the table below. Insults, Compliments, and Neutral Appearance Comments (Males commenting) Nature of comment Males about males Males about females Compliments 52 106 Insults 41 15 Totals 93 121 (a) Graphically present these data by constructing a comparative bar chart that would allow you to compare the comments about males and females. (b) Using the information in the table, write a few sentences about how the comments differ for male recipients and female recipients.

An outlier is a data value that is unusually far from the rest of the values in a data set.

A time series plot is a graph of data that has been gathered at different points in time.

In a scatter plot, both the horizontal and vertical axes must start at zero.

A report in the Des Moines Register presented the average number of years of teaching experience for the teachers in elementary schools in Des Moines, Iowa. These data appear in the table below. School Average Years Exper. School Average Years Exper. School Average Years Exper. School Average Years Exper. Adams 13.8 Hanawalt 12.7 McKee 17.5 Phillips 10.5 Capitol View 9.7 Hillis 17 McKinley 5.6 Pleasant 12.8 Hill Cattell 8.5 Howe 14.9 Mitchell 6.2 River Woods 5.9 Douglas 13.8 Hubbell 15.1 Monroe 16.2 Stowe 16.5 Downtown 7.0 Jackson 16.8 Moore 16.6 Studebaker 18.4 Edmunds 8.4 Jefferson 19.2 Morris 9.9 Wallace 4.8 Findley 14.9 King 7.0 Moulton 8.6 Willard 9.7 Garton 9.3 Longfellow 9.8 Oak Park 11.4 Windson 17.7 Granger 17.2 Lovejoy 9.9 Park 11.4 Woodlawn 17 Greenwood 14 Madison 20.8 Perkins 11.2 Wright 12.9 (a) Sketch a histogram for these data, using the following class intervals: 0 to <4 4 to <8 , etc. (b) Describe the distribution of the average number of years of teaching experience, and note any unusual features.

If the upper tail of a distribution stretches out farther than the lower tail, the distribution is negatively skewed.

A unimodal set of data is one that contains only one variable.

A report in the Des Moines Register presented on the percentages of students who qualify for Free/Reduced lunch programs in the elementary schools in Des Moines, Iowa. These data appear in the table below. School \% F/R School \% F/R School \% F/R School \% F/R Adams 64 Hanawalt 14 McKee 55 Phillips 27 Capitol View 78 Hillis 35 McKinley 78 Pleasant Hill 17 Cattell 55 Howe 49 Mitchell 64 River Woods 48 Douglas 45 Hubbell 31 Monroe 52 Stowe 56 Downtown 8 Jackson 60 Moore 42 Studebaker 30 Edmunds 83 Jefferson 5 Morris 54 Wallace 80 Findley 64 King 71 Moulton 88 Willard 82 Garton 53 Longfellow 84 Oak Park 59 Windson 37 Granger 52 Lovejoy 66 Park Avenue 38 Woodlawn 40 Greenwood 38 Madison 58 Perkins 54 Wright 29 (a) Sketch a histogram for these data, using the following class intervals: 20 t 0 t 0 to <20 20 to <40 , etc. (b) Describe the distribution of Free/Reduced eligibility percents, and note any unusual features.

Desert organisms must cope with extreme and variable conditions. Their coping strategies frequently involve retreating to a sub-surface refuge. Researchers in New Mexico, investigating the underground shelter choices by Gila Monsters (Heloderma suspectum), hypothesized that depth might be a factor. They reasoned that deeper shelters would be less susceptible to extremes of heat and cold and thus depth would be preferred in a shelter. Depth data for 20 chosen shelters and the 20 nearest available shelters not chosen are presented in the table at right. Shelter Depths (cm) Chosen Nearest Chosen Nearest 94 54 33 32 89 6 15 14 32 57 27 7 76 50 27 32 65 46 85 28 30 41 52 52 68 43 80 50 84 59 33 55 10 55 79 69 58 53 71 55 a) Display these data using a comparative (back-to-back) stem-and-leaf plot. Use the stems shown below, and be sure to include all information needed to compare the two distributions. |1| |2| |3| |4| |0| |0| |1| |2| |3| |4| |5| |6| |7| |8| |9| |5| |6| |7| |8| |9| (b) Describe the similarities and differences between the chosen and not chosen shelter depths. (c) Are these data consistent with the researchers' expectations? Explain, using specific aspect(s) of your plot in part (a).

D Desert organisms must cope with extreme and variable conditions. Their coping strategies frequently involve retreating to a sub-surface refuge. Researchers in New Mexico, investigating the underground shelter choices by Gila Monsters (Heloderma suspectum), hypothesized that depth might be a factor. They reasoned that deeper shelters would be less susceptible to extremes of heat and cold and thus depth would be preferred in a shelter. Depth data for 20 chosen shelters and 20 available shelters not chosen are presented in the table at right. Shelter Depths (cm) Chosen Nearest Chosen Nearest 94 54 33 32 89 6 15 14 32 57 27 7 76 50 27 32 65 46 85 28 30 41 52 52 68 43 80 50 84 59 33 55 10 55 79 69 58 53 71 55 a) Display these data using a comparative (back-to-back) stem-and-leaf plot. Use the stems shown below, and be sure to include all information needed to compare the two distributions. |1| |2| |3| |4| |0| |1| |2| |3| |4| |5| |6| |7| |8| |9| |5| |6| |7| |8| |9| (b) Describe the similarities and differences between the chosen and not chosen shelter depths. (c) Are these data consistent with the researchers' expectations? Explain, using specific aspect(s) of your plot in part (a).

Marine biologists have reported the discovery of a new species of fish in the Western North Atlantic. Data on the head length (n=41) and pelvic fin length (n=30) are shown below. a) Describe the distributions of these two variables using appropriate statistical terms. b) The distribution of head lengths appears to be rather strange. What do you think might account for the shape of this distribution?