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1. Review of Top 10 Conceptsin 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