Outline Graphical Methods l Graphical versus Numerical Methods

Outline: Graphical Methods l Graphical versus Numerical Methods l Frequency distributions (tables) l Histogram l Stem-and-leaf plot l Box plot l Pie chart l Scatter plot (c) 2007 IUPUI SPEA K 300 (4392)

Graphical vs. Numerical Methods l Graphical methods: Intuitive, easy to understand l Difficult to construct manually l Useful to find overall patterns l l Numerical methods: Require some knowledge l Provide more objective ways of describing data l (c) 2007 IUPUI SPEA K 300 (4392)

Frequency Table l Class and frequency l Mutually exclusive and exhaustive Class limits should not overlap l Class should not be omitted l l Class limits (boundaries) l Class width l Should be uniform (equal width) l Class midpoint (c) 2007 IUPUI SPEA K 300 (4392)

Steps l Determine the number of classes Find minimum and maximum values l Select the number of classes l Find the limits and boundaries l l Tally the data to get frequencies l Relative frequency = freq/N l Cumulative frequency (c) 2007 IUPUI SPEA K 300 (4392)

Example l Cereal Calories, question 15 on page 59 l Range: 190 (= 270 - 80) l 5 classes; 50 class width l Class midpoint: 125, 175… class | Freq. Percent Cum. ------------+-----------------<=100 | 8 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 (c) 2007 IUPUI SPEA K 300 (4392)

Bar Chart (c) 2007 IUPUI SPEA K 300 (4392)

Histogram l Continuous vertical bars for density (c) 2007 IUPUI SPEA K 300 (4392)

Histogram Polygon, Oglive Frequency polygon connects midpoints of classes l Ogive is the cumulative frequency graph l Histogram shapes, Figure 2 -8 on page 56 l (c) 2007 IUPUI SPEA K 300 (4392)

Stem-and-leaf plot l l l 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* 2* 3* 4* 5* 6* 7* | | | | 2788 001489 1367 148 0 0 6 (c) 2007 IUPUI SPEA K 300 (4392)

Box plot l l l Minimum, maximum 25 th and 75 th percentile (1 th and 3 th quartile) Mean, medium (c) 2007 IUPUI SPEA K 300 (4392)

Pie chart l Degree=(frequency/N)*360 (c) 2007 IUPUI SPEA K 300 (4392)

Scatter Plot (Q 14 on page 89) l l To examine the relationship between two variables Positive, negative, linear, exponential, … (c) 2007 IUPUI SPEA K 300 (4392)

Misleading Graphs l Page 70 -73 l Irrelevant scales l Not report units and labels. l Irrelevant type of graphs l Irrelevant perspective (c) 2007 IUPUI SPEA K 300 (4392)

Perspectives (c) 2007 IUPUI SPEA K 300 (4392)