1. (c) 2007 IUPUI SPEA K300 (4392) Outline: Graphical Methods Graphical versus Numerical Methods Frequency distributions (tables) Histogram Stem-and-leaf plot Box plot Pie chart Scatter plot

2. (c) 2007 IUPUI SPEA K300 (4392) Graphical vs. Numerical Methods Graphical methods: Intuitive, easy to understand Difficult to construct manually Useful to find overall patterns Numerical methods: Require some knowledge Provide more objective ways of describing data

3. (c) 2007 IUPUI SPEA K300 (4392) Frequency Table Class and frequency Mutually exclusive and exhaustive Class limits should not overlap Class should not be omitted Class limits (boundaries) Class width Should be uniform (equal width) Class midpoint

4. (c) 2007 IUPUI SPEA K300 (4392) Steps Determine the number of classes Find minimum and maximum values Select the number of classes Find the limits and boundaries Tally the data to get frequencies Relative frequency = freq/N Cumulative frequency

5. (c) 2007 IUPUI SPEA K300 (4392) Example Cereal Calories, question 15 on page 59 Range: 190 (= 270 - 80) 5 classes; 50 class width Class midpoint: 125, 175… class | Freq. Percent Cum. ------------------------+----------------------------------- <=100 | 8 17.39 17.39 100-150 | 14 30.43 47.82 150-200 | 13 28.26 76.08 200-250 | 9 19.57 95.65 250-300 | 2 4.35 100.00 ------------------------+----------------------------------- Total | 46 100.00

6. (c) 2007 IUPUI SPEA K300 (4392) Bar Chart

7. (c) 2007 IUPUI SPEA K300 (4392) Histogram Continuous vertical bars for density

8. (c) 2007 IUPUI SPEA K300 (4392) Histogram Polygon, Oglive Frequency polygon connects midpoints of classes Ogive is the cumulative frequency graph Histogram shapes, Figure 2-8 on page 56

9. (c) 2007 IUPUI SPEA K300 (4392) Stem-and-leaf plot Provide much useful information Sort data in the ascending order Determine leading digits Record data by putting their trailing digit Question 15 on page 79 Stem-and-leaf plot for tax 1* | 2788 2* | 001489 3* | 1367 4* | 148 5* | 0 6* | 0 7* | 6

10. (c) 2007 IUPUI SPEA K300 (4392) Box plot Minimum, maximum 25 th and 75 th percentile (1th and 3th quartile) Mean, medium

11. (c) 2007 IUPUI SPEA K300 (4392) Pie chart Degree=(frequency/N)*360

12. (c) 2007 IUPUI SPEA K300 (4392) Scatter Plot (Q14 on page 89) To examine the relationship between two variables Positive, negative, linear, exponential, …

13. (c) 2007 IUPUI SPEA K300 (4392) Misleading Graphs Page 70-73 Irrelevant scales Not report units and labels. Irrelevant type of graphs Irrelevant perspective

14. (c) 2007 IUPUI SPEA K300 (4392) Perspectives