Chapter 2: Organizing Data

PCBs and Pelicans. Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United States in 1979 and by the Stockholm Convention on Persistent Organic Pollutants in 2001. One study, published in 1972 by R. W. Risebrough, is titled "Effects of Environmental Pollutants Upon Animals Other Than Man" (Proceedings of the 6ed Berkeley Symposium on Mathematics and Statistics, VI, University of California Press, pp. 443-463). In that study, 60 Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBs, in parts per million (ppm). Following is a relative-frequency histogram of the PCB concentration data.

Adjusted Gross Incomes. The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in the document Siarisuics of Income, Individual Income Tax Reforms. The following relative-frequency histogram shows one year's individual income tax returns for adjusted gross incomes of less than 50,000.

Cholesterol Levels. According to the National Health and Nutrition Examination Survey, published by the Centers for Disease Control and Prevention, the average cholesterol level for children between 4 and 19 years of age is 165mg /dl. A pediatrician who tested the cholesterol levels of several young patients was alarmed to find that many had levels higher than 200mg / dL. The following relative frequency histogram shows the readings for some patients who had high cholesterol levels.

Sickle Cell Disease. A study published by E. Anionwu et al. in the British Medical Journal (Vol, 282, pp .283-286) measured the steady-state hemoglobin levels of patients with three different types of sickle cell disease. Following is a stem-and-leaf diagram of the data.

Stays in Europe and the Mediterranean. The Bureau of Economic Analysis gathers information on the length of stay in Europe and the Mediterranean by U.S. travelers. Data are published in the Survey of Current Bussiness. The following stem-and-leaf diagram portrays the length of stay, in days, of a sample of 36 U.S. residents who traveled to Europe and the Mediterranean last year.

Top 10 Green Cars. The following table presents information on the Kelley Blue Book's "10 Best Green Cars of 2013." Note that mpg and mpge are abbreviations for miles per gallon and miles per gallon equivalent, respectively. Identify the type of data provided by the information in each column of the table. [SOURCE: "10 Best Green Cars of 2013." Published by the Kelley Blue

Old Faithful. Old Faithful is a geyser in Yellowstone National Park that erupts at relatively predictable intervals. Since 2000, the eruptions of Old Faithfull occur on average every 90 minutes. Information on the daily eruptions of Old Faithful can be found on the website of The Geyser Observation and Study Association (GOSA). The following data provide the times between eruptions, in minutes, for Old Faithful over a two-day period.

a. Use cut point grouping with a first class of $60-$under $70$to construct a frequency histogram of the times between eruptions.

b. Identify the shape of the distribution with regard to modality.

c. Identify the shape of the distribution with regard to symmetry (or non-symmetry).

d. If the distribution is unimodal and nonsymmetric, classify it as either right-skewed or left-skewed.

Old Faithful. Old Faithful is a geyser in Yellowstone National Park that erupts at relatively predictable intervals. Since 2000, the eruptions of Old Faithfull occur on average every 90 minutes. Information on the daily eruptions of Old Faithful can be found on the website of The Geyser Observation and Study Association (GOSA). The following data provide the times between eruptions, in minutes, for Old Faithful over a two-day period.

a. Use cutpoint grouping with a first class of 60 -under 70 to construct a frequency histogram of the times between eruptions.

b. Identify the shape of the distribution with regard to modality.

c. Identify the shape of the distribution with regard to symmetry (or nonsymmetry).

d. If the distribution is unimodal and nonsymmetric, classify it as either right skewed or left skewed.

Snow Goose Nests. In the article "Trophic Interaction Cycles in Tundra Ecosystems and the Impact of Climate Change" (BioScience, Vol. 55, No. 4, pp. 311-321), R. Ims and E. Fuglei provided an overview of animal species in the northern tundra. One threat to the snow goose in arctic Canada is the lemming. Snowy owls act as protection to the snow goose breeding grounds. For two years that are 3 years apart, the following graphs give relative frequency histograms of the distances, in meters, of snow goose nests to the nearest snowy owl nest.

For each histogram do the following:

(a) Identify the shape of the distribution with regard to modality.

(b) Identify the shape of the distribution with regard to symmetry (non-symmetry).

(c) If the distribution is unimodal and non-symmetric, classify it as either right-skewed or left-skewed.

(d) Compare the two distributions.

Snow Goose Nests. In the article "Trophic Interaction Cycles in Tundra Ecosystems and the Impact of Climate Change" (BioScience, Vol. 55, No, 4, pp, 311-321), R. Ims and E. Fuglei provided an overview of animal species in the northern tundra. One threat to the snow goose in arctic Canada is the lemming. Snowy owls act as protection to the snow goose breeding grounds. For two years that are 3 years apart, the following graphs give relative frequency histograms of the distances, in meters, of snow goose nests to the nearest snowy owl nest.