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STATISTICS

STATISTICS. Chapter 12. Definitions. Descriptive Statistics. Inferential Statistics. Data – numerical information Statistics – method for collecting, organizing, analyzing, and presenting data as well as interpreting that data and drawing conclusions from it.

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STATISTICS

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  1. STATISTICS Chapter 12

  2. Definitions Descriptive Statistics Inferential Statistics Data – numerical information Statistics – method for collecting, organizing, analyzing, and presenting data as well as interpreting that data and drawing conclusions from it

  3. Sampling, Frequency Distributions, and Graphs Section 12.1

  4. Definitions Population – set containing all the people or objects whose properties are to be described by the data collector Sample – subset of a population

  5. Example What is the population? all BHS students What is the sample? the surveyed students Consider all the students at Brighton High School (approximately 1400 students). You wish to determine if most students enjoy their math class. You randomly select 20 students from each of the 5 lunch shifts and ask them, collecting the responses.

  6. Example What is the population? BHS athletes What is the sample? BHS captains Consider all the students at Brighton High School who play a sport for BHS. You want to know their feelings on sports practice during school versus after school. You speak to the captains of each sport.

  7. A Story What went wrong? In 1936 Literary Digest magazine mailed out 10 million ballots about the presidential election. The ballots went to people from their subscription list, car owners, and people listed in telephone books. Based on the results, they predicted a landslide victory for Alf Landon over Franklin Roosevelt. But the landslide victory went to FDR! As a result of this fiasco as well as the Depression, the magazine folded in 1937.

  8. A Story What went wrong? The ballots went to the rich, who were more likely to vote for the Republican candidate. It was not a random sample of people!

  9. Definitions Random Sample – sample obtained in such a way that every element in the population has an equal chance to be selected for the sample

  10. Example drawing names from a hat YES calling in to a talk show NO Would this be considered random?

  11. Example • Descriptive Statistics • Data will be: • Collected • Organized • Presented P • randomly survey people who live in the oceanfront condominiums in the city • survey the first 200 people whose names appear in the city’s telephone directory • randomly select neighborhoods of the city and then randomly survey people within the selected neighborhoods Hotel owners in a large city are interested in how the city’s citizens feel about casino gambling. Which of the following would be the most appropriate way to select a sample?

  12. Example 12, 14, 13, 14, 16, 14, 14, 17, 13, 10, 13, 18, 12, 15, 14, 15, 15, 14, 14, 13, 15, 16, 15, 12, 13, 16, 11, 15, 12, 13, 12, 11, 13, 14, 14 A random sample of 35 ten-year-old boys is measured for height and re-measured each year until they reach eighteen. The age of maximum yearly growth was found:

  13. Example Frequency Distribution data value a two-column table of data values and the number of times each occurs age of maximum yearly growth 12, 14, 13, 14, 16, 14, 14, 17, 13, 10, 13, 18, 12, 15, 14, 15, 15, 14, 14, 13, 15, 16, 15, 12, 13, 16, 11, 15, 12, 13, 12, 11, 13, 14, 14 data item

  14. Example Grouped Frequency Distribution Frequency Distribution Etc. a two-column table of data values organized into groups (classes) 82 47 75 64 57 82 63 93 76 68 84 54 88 77 79 80 94 92 94 80 94 66 81 67 75 73 66 87 76 45 43 56 57 74 50 78 71 84 59 76 Test Scores:

  15. Definitions • Descriptive Statistics • Data will be: • Collected • Organized • Presented P P upper limit 99 lower limit 90 class width 90 – 80 = 10

  16. Return to Example Histogram Bar graph with bars that touch age of maximum yearly growth does not start at zero

  17. SameExample Frequency Polygon Line graph made by connecting the midpoint of each bar in the histogram and touching axis age of maximum yearly growth

  18. Definitions Stem-and-leaf plot – a way to display data where it is organized by place value and so that the shape of the distribution (spread of data) is visible

  19. Return to Example 82 47 75 64 57 82 63 93 76 68 84 54 88 77 79 80 94 92 94 80 94 66 81 67 75 73 66 87 76 45 43 56 57 74 50 78 71 84 59 76 Separate data into parts – for this example, the stem will be the tens’ digit and the leaf will be the one’s digit. Test Scores:

  20. Return to Example 82 47 75 64 57 82 63 93 76 68 84 54 88 77 79 80 94 92 94 80 94 66 81 67 75 73 66 87 76 45 43 56 57 74 50 78 71 84 59 76 Stems Leaves • 4 • 5 • 6 • 7 • 8 • 9 3 5 7 0 4 6 7 7 9 3 4 6 6 7 8 1 3 4 5 5 6 6 6 7 8 9 0 0 1 2 2 4 4 7 8 2 3 4 4 4 Test Scores:

  21. Looks 9 times bigger! Example Actually about 1.5 times bigger! From 1978 to 1985 there has been huge changes in fuel economy standards for cars. The information is misleading but not inaccurate. Deceptions in Visual Displays of Data

  22. Example What is misleading about this graph? How much the purchasing power of the dollar actually diminished was not as bad as shown…because they used area to illustrate. This is half… This is ¼ or 0.25

  23. The End “There are three kinds of lies: lies, damned lies, and statistics.” – Benjamin Disraeli HOMEWORK 12.1 pg 641 # 1 – 31 odd

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