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1-23 - CHAPTER 1 — EXPLORING DATA BY GRAPHICAL METHODS...

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Unformatted text preview: CHAPTER 1 — EXPLORING DATA BY GRAPHICAL METHODS 1.1 The Science of Statistics Statistics is the discipline, or the science, of gathering data, describing data, and drawing conclusions (making inferences) from data. Example 1: Winter Olympics In 1994, 27.8% of U. S. households tuned into the CBS broadcast of the Winter Olympic Games In Lillehammer, Norway. This represented a 49% increase over those who viewed the CBS broadcast of the 1992 Winter Olympic Games in Albertville, France. Since only a sample of the overall population was Sampled, these numbers are estimates. Using statistical inference, what conclusions can we draw from this numerical information? [6(an ’87?) 0F hOU5¢holO‘S. «QM—l: Is sample 5IZ¢Z Hm.) we 3 the Sample chosen 2 There are two aspects to the discipline of statistics. Descriptive statistics are the techniques for graphically representing data and numerically summarizing them. Inferential statistics are the techniques used to infer information about the population using the information from the sample. Example 2: More Math = More Money? Studies have shown that taking more math classes in school results in a higher paying career. Can we claim a cause-and-effect relationship between the treatment (taking more math classes" In school) and the response (higher salary)? Is there a positive association between the two variables? cause-v qfld c-C’Qe'ct 7, No! P05 i-éIK/e a sacei‘q‘éi‘on 7. Ya 6' Example 3: Body Weight vs. Brain Weight (Section 1.1, Exercise #6, p. 12) The following data show the brain weights (in grams) and body weights (in kilograms) of selected animals (extant and extinct). a. Rank the animals from largest (1) to smallest (19) according to the body weight and then do the same for the brain weight. b. Are the two rankings positively associated? Yes. c. Do you notice that a certain group of animals seems very different in the - closeness of matching of their ranks? (Statisticians call data points that are very different from the main body of the data outliers.) Dino$quf$ -- \fefy large loaf Effie/l bra/345 HLM’MI’lé ‘{ Chum/96 -- ”0’6 Very JOI<3\ bqiblj lam/”5. ~ Chapter 1 — Exploring Data Body weight Body weight Brain weight Brain weight Species gkg) rank gg) rank Mountain beaver 1.35 “5 8.1 l 5 Grey wolf 36.33 i ‘ 119.5 I 0 Guinea pig 1.04 l (a 5.5 i b Diplodocus 11,700 1 ' 50 3 ’5 Asian elephant 2547 5 4603 7- Potar monkey 10 12 115 l l Giraffe 529 6: 680 “l Gorilla 207 7 406 . 6 Human 62 q 1320 S African elephant 6654 Li 5712 l Triceratops .9400 ’5 70 ‘l 2 Rhesus monkey 6.8 l ’6 179 7 Mouse 0.023 [4 0.4 1 cl Rabbit 2.5 l 1‘ 12.1 i 1.; Jaguar 100 o _ 157 g Chimpanzee 52.16 1% 440 e Brachiosaurus 87,000 l 154.5 cl Rat 0.28 1 '7 1.9 '8 . Mole 0.122 1 3 i7 Source: H. J. Jerison. 1973. Evaluation oft/7e Brain and Inte/ligence. New York: Academic Press. Types of Variables: Chapter 1 - Exploring Data Example 4: Classifying Variables (Section 1.1, Exercise #3, p. 11) Classify each of the following variables as either discrete or continuous numerical, nonranked categorical, or ranked categorical. a. blood type N C- b. grade—point average CN IQ R C number of children D N . occupation M C, state in which a person’s legal residence is N C systolic blood pressure C. N I :Lprhmgp . letter grade in a college course R C. i. college major NC. Example 5: Snoring and Heart Disease (Section 1.1, Exercise #5, p.12) A survey was conducted by the Brit/Sh Medical Journal to study the relationship between snoring and heart disease. Heart , Occasional Snore nearly Snore every Disease Nonsnorers snorers ' every night night Total Yes 24 35 2 1 3O 1 10 N0 1355 603 192 224 2374 Total 1379 ‘ 638 213 254 2484 Source: P. G. Norton and E. V. Dunn. 1985. Snoring as a risk factor for the disease: An epidemiological survey. Brit/19h Medical Journa/, 291: 630-632. - I ”Live E Hq9b q .8670 l ‘ ' 8‘90 a. Which of the four categories of snorers is most prone to heart disease? Hint: Would it be right to say that occasional snorers are most prone to heart disease because out of the 110 persons who have heart disease, the greatest number (35) are occasional snorers and no other category has such a high number of - snorers with heart disease? Explain. CcmP‘V‘L 07°, Snore every m'aln‘é .- b. Is there any kind of relationship between the degree of snoring and being prone to heart disease? Y86~ MDK: 6flofe: More (H's k c. Suppose a behavioral psychologist tells a person who snores often that he can condition him not to snore. Is this likely to reduce that person’s risk of heart disease? In other words, is it plausible that snoring is the cause of heart disease? If yOu do not think so, give another possible explanation of why frequent snorers have more heart disease than infrequent snorers. N015 Cquéc-an0l~e#ecé. ~ obesfiéx/ 7 " \‘ cask/[C ~ alcohol Mimic: — 517855 Chapter 1 —- Exploring Data 1.2 Displaying Small Sets of Numbers: Dotplots and Stem-and-Leaf Displays Graphs help us visualize patterns and trends in data that are hard to see when looking at the raw data. One way of graphing data visually is to construct a dotplot. Dotplots are useful when we have both repeated values and numbers that aren’t too spread out. Example 6. Test Scores Below7 are 45 test scores. Create a 7dotplot9 of the data set. 100 86 80 9O 97 75 I 86 82 95 86 81 98 93 86 84 95 9O 85 91 87 79' , 85 95 80 92 . 95 95 96 85 94 . 89 80 96 94 96 97 93 7O 80 90 v 100 Another way of graphing data visually is the stem-and-leaf plot (also called a stemplot). A mixture of a table and graph, a stem-and—leaf plot displays the basic distribution or pattern of variation'of the data. Example 7. Test Scores, continued Using the 45 test scores given in Example 1, construct a st-em and— leaf plot. 7 ZiHEE‘Efi 8 ooor 7. Li 5555ccce<p7ci Cl 00 i z 53 H 44 555556436778”; [DO ...
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