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Review of Top 10 Concepts in Statistics

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Review of Top 10 Concepts in Statistics

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    1. Review of Top 10 Concepts in Statistics NOTE: This Power Point file is not an introduction, but rather a checklist of topics to review

    2. Top Ten #1 Descriptive Statistics

    3. Measures of Central Location Mean Median Mode

    4. Mean Population mean == Sx/N = (5+1+6)/3 = 12/3 = 4 Algebra: Sx = N* = 3*4 =12 Sample mean = x-bar = Sx/n Example: the number of hours spent on the Internet: 4, 8, and 9 x-bar = (4+8+9)/3 = 7 hours Do NOT use if the number of observations is small or with extreme values Ex: Do NOT use if 3 houses were sold this week, and one was a mansion

    5. Median Median = middle value Example: 5,1,6 Step 1: Sort data: 1,5,6 Step 2: Middle value = 5 When there is an even number of observation, median is computed by averaging the two observations in the middle. OK even if there are extreme values Home sales: 100K,200K,900K, so mean =400K, but median = 200K

    6. Mode Mode: most frequent value Ex: female, male, female Mode = female Ex: 1,1,2,3,5,8 Mode = 1 It may not be a very good measure, see the following example

    7. Measures of Central Location - Example Sample: 0, 0, 5, 7, 8, 9, 12, 14, 22, 23 Sample Mean = x-bar = Sx/n = 100/10 = 10 Median = (8+9)/2 = 8.5 Mode = 0

    8. Relationship Case 1: if probability distribution symmetric (ex. bell-shaped, normal distribution), Mean = Median = Mode Case 2: if distribution positively skewed to right (ex. incomes of employers in large firm: a large number of relatively low-paid workers and a small number of high-paid executives), Mode < Median < Mean

    9. Relationship contd Case 3: if distribution negatively skewed to left (ex. The time taken by students to write exams: few students hand their exams early and majority of students turn in their exam at the end of exam), Mean < Median < Mode

    10. Dispersion Measures of Variability How much spread of data How much uncertainty Measures Range Variance Standard deviation

    11. Range Range = Max-Min > 0 But range affected by unusual values Ex: Santa Monica has a high of 105 degrees and a low of 30 once a century, but range would be 105-30 = 75

    12. Standard Deviation (SD) Better than range because all data used Population SD = Square root of variance =sigma =s SD > 0

    13. Empirical Rule Applies to mound or bell-shaped curves Ex: normal distribution 68% of data within + one SD of mean 95% of data within + two SD of mean 99.7% of data within + three SD of mean

    14. Standard Deviation = Square Root of Variance

    15. Sample Standard Deviation

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