1. Chapter 3 Data Description Section 3-3 Measures of Variation

2. Range

3. Variance

4. Sample Variance

5. Sample Standard Deviation

6. Shortcut

7. Find the range. Section 3-3 Exercise #7

8. Is the data consistent or does it vary? Explain.

9. Finding the Sample Variance and Standard Deviation for Grouped Data

10. 2539-602 1475-539 0411-474 2347-410 0283-346 5219-282 0155-218 291-154 1327-90 f Number Section 3-3 Exercise #21

11. Class f

13. Section 3-3 Exercise #33

15. Chebyshev’s theorem

16. The Empirical (Normal) Rule Chebyshev’s theorem applies to any distribution regardless of its shape. However, when a distribution is bell-shaped (or what is called normal), the following statements, which make up the empirical rule, are true. Approximately 68% of the data values will fall within 1 standard deviation of the mean. Approximately 95% of the data values will fall within 2 standard deviations of the mean. Approximately 99.7% of the data values will fall within 3 standard deviations of the mean.

18. Section 3-3 Exercise #41

20. Chapter 3 Data Description Section 3-4 Measures of Position

21. A z score or standard score for a value is obtained by subtracting the mean from the value and dividing the result by the standard deviation. The symbol for a standard score is z. The formula is

22. Section 3-4 Exercise #13

23. Percentile Formula

24. Section 3-4 Exercise #22

26. Section 3-4 Exercise #23

28. Chapter 3 Data Description Section 3-5 Exploratory Data Analysis

29. The Five-Number Summary and Boxplots

30. A boxplot is a graph of a data set obtained by drawing a horizontal line from the minimum data value to Q1, drawing a horizontal line from Q3 to the maximum data value, and drawing a box whose vertical sides pass through Q1 and Q3 with a vertical line inside the box passing through the median or Q2.

31. Minimum: Q1:Q1: Median: Q3:Q3: Maximum: Interquartile Range: Data arranged in order: Identify the five number summary and find the interquartile range. 8, 12, 32, 6, 27, 19, 54 Section 3-5 Exercise #1

32. Section 3-5 Exercise #9

33. 1. a. If the median is near the center of the box, the distribution is approximately symmetric. b. If the median falls to the left of the center of the box, the distribution is positively skewed. c. If the median falls to the right of the center, the distribution is negatively skewed. 2. a. If the lines are about the same length, the distribution is approximately symmetric. b. If the right line is larger than the left line, the distribution is positively skewed. c. If the left line is larger than the right line, the distribution is negatively skewed. Information Obtained from a Boxplot

34. 9.88.013.94.43.921.7 15.93.211.724.834.117.6 Section 3-5 Exercise #15

35. Data arranged in order :

36. 50,000 52,435 62,850 66,500 77,700 78,008 92,000 125,628 United States 46,563 56,242 102,014 105,944 274,026 311,539 South America Section 3-5 Exercise #16