Chapter 12: Statistics
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1 Chapter 12: Statistics Statistics is a method for collecting, organizing, analyzing, and interpreting data (descriptive statistics), as well as making generalizations and drawing conclusions from data (inferential statistics). ex. "In 1 week, the average TCC student uses an ATM 2.6 times." (from a survey of 60 students) ex. "It is estimated that 62% of American children would not like to be president of the United States." (from a survey of 1,172 American children ages 6 14) John Gaunt's analysis of Bills of Mortality (weekly publication put out by parish clerks listing births, christenings, deaths and their causes) in 1662 represents the first time that social and biological phenomena were interpreted from mass data. Some of Gaunt's conclusions are: The number of male births was greater than the number of female births; "the one exceeds the other by about a thirteenth part." "More men die violent deaths than women." Because the number of adult men is approximately equal to the number of adult women, monogamy is more agreeable to the Law of Nature." Few people starve. "the vast numbers of Beggars, swarming up and down this city (London), do all live,.." Sep 15 6:30 AM 1
2 Section 12.1: Sampling, Frequency Distributions, and Graphs Objectives 1 4 Population: set being studied Sample: subset of population P S If a sample is to be used to make generalizations about a population, it should be a representative sample (have the same characteristics typical of the target population) and it must be a random sample (every member of the population has an equal chance of being selected for the sample). ex. A. C. Nielsen Co. uses a random sample of 5,000 households to draw conclusions about ~ 94 million households. Hw.#2: The American Association of Nurse Anesthetists Journal (Feb. 2000) published the results of a study on the use of herbal medicines before surgery. Of 500 surgical patients who were randomly selected for the study, 51% used herbal or alternative medicines prior to surgery. a. Describe the population and the sample of this study. b. Is the sample representative of the population? c. For each patient, what variable is measured? Are the data quantitative (numerical) or qualitative (non numerical categories)? Sep 15 6:31 AM 2
3 Appropriate Sampling Techniques ex. Assign a number to each member in population and use a random number generator (computer or calculator) to randomly select numbers. Call in polls on TV or radio and voluntary mail in polls have a built in bias. Telephone directories are not indicative of a region's population. Names listed alphabetically must be used randomly. ex. A newspaper wants to find out what percentage of its readers follow the weekly gardening column and what is their opinion of the column. Which one of the following procedures would be most appropriate for obtaining a sample of the newspaper's readers? a. Survey the first 100 people in an alphabetical listing of subscribers. b. Serving every fifth person arriving to eat at the food court in the local mall. c. Survey a random sample of readers from a list of all subscribers. d. Send out questionnaires to the local garden club. Sep 15 6:34 AM 3
4 Frequency Distributions Frequency: number of times a data value occurs Frequency Distribution: table used to present data in a condensed form left column = data values right column = frequencies Hw.#10: A random sample of 30 male college students is selected. Each student is asked his height (to the nearest inch). The heights are as follows: 72, 70, 68, 72, 71, 71, 71, 69, 73, 71, 73, 75, 66, 67, 75 74, 73, 71, 72, 67, 72, 68, 67, 71, 73, 71, 72, 70, 73, 70 Construct a frequency distribution for the data. Sep 15 6:34 AM 4
5 Grouped Frequency Distribution: reduce number of rows by creating groups or classes. Class Width: number of values in each class Lower Class Limit: leftmost number in each class Upper Class Limit: rightmost number in each class Hw.#20: The IQ scores of 70 students enrolled in a liberal arts course at a college are as follows: 102, 100, 103, 86, 120, 117, 111, 101, 93, 97, 99, 95, 95, 104, 104, 105, 106, 109, 109, 89, 94, 95, 99, 99, 103, 104, 105, 109, 110, 114, 124, 123, 118, 117, 116, 110, 114, 114, 96, 99, 103, 103, 104, 107, 107, 110, 111, 112, 113, 117, 115, 116, 100, 104, 102, 94, 93, 93, 96, 96, 111, 116, 107, 109, 105, 106, 97, 106, 107, 108. Construct a grouped frequency distribution for the data. Use for the first class and use the same width for each subsequent class. Sep 15 6:37 AM 5
6 Answer the following questions about the data: What is the class width? What is the upper class limit for the third class? How many students had an IQ of at least 100? How many students had an IQ of at most 109? Sep 15 6:37 AM 6
7 Histograms and Frequency Polygons Histogram: heights of rectangles (or bars) represent frequencies Frequency Polygon: heights of dots indicate frequencies, lines connect the dots, and line is "tied down" to the horizontal axis. ex. Gather data on the number of hours you slept last night (round to nearest hour). Construct a frequency distribution table. Construct a histogram and a frequency polygon. Sep 15 6:40 AM 7
8 I don't have room on this graph to also do a histogram. Frequency Polygon Number of Hours You Slept Last Night n=23 Note: You will not construct graphs, just interpret them. Sep 15 6:42 AM 8
9 frequency (number of students) This is a really crummy histogram. Each bar is supposed to be the same width, and each is supposed to have its "number" right in the middle of the bottom (and the red dot right in the middle of the top). data points (number of hours slept). Number of Hours You Slept Last Night n=23 Sample size (Data collection was faulty due to rowdy students)! Note: You will not construct graphs, just interpret them. Oct 6 11:59 AM 9
10 Stem and Leaf Plots: data items are separated into 2 parts Stem = tens' digit Leaf = units' digit Hw.#26: As of 2007, the following are the ages, in chronological order, at which U.S. presidents were inaugurated: 57, 61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, 52, 56, 46, 54, 49, 50, 47, 55, 55, 54, 42, 51, 56, 55, 51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54 Construct a stem and leaf plot for the data. Stem Leaves Sep 15 6:43 AM 10
11 ex. The amount of time it takes for 3 leading pain relievers to reach your bloodstream is as follows: Brand A 480 seconds Brand B 500 seconds Brand C 490 seconds The vertical scale "inflates" or "deflates" a trend! See text examples 1 5. Sep 15 6:45 AM 11
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