1. Stem – and – Leaf plots: It’s Not a Botany Activity! Dr. Cheryl Malm Northwest Missouri State University Dr. Patricia Lucido Rockhurst University 1

2. Visualizing Data Analysis begins by trying to get a “good picture” of the data – For most data sets, there is more than one appropriate and informative way to display the data – Often valuable to see the same data plotted in several ways University of Washington: Elementary Quantitative Literacy Program 2

3. Types of data displays Line Plots Histograms Stem and Leaf Plots Box and Whisker Plots Scatter Plots Time Series Plots 3

4. Stem and Leaf Plots vs. Histograms Both group the data into intervals Both display the distribution of the data Both display the shape of the distributions Stem and Leaf Plots retain the original data where histograms only show the “groups” of the data 4

5. Temperatures for June 50, 57, 61, 62, 64, 59, 65, 65, 67, 62, 65, 70, 71, 70, 68, 73, 69, 76, 77, 79, 80, 80, 82, 77, 79, 82. 80. 83. 87. 84 What is the average temperature? What is the median temperature? What temperature is it most of the time? 5

6. Histogram \6

7. 7

8. Stem and Leaf Plot 8 StemLeaf 50 7 9 61 1 2 2 4 5 5 5 7 8 9 70 0 1 3 6 7 7 9 9 80 0 0 2 2 3 7 Key: 5 | 0 means 50

9. Split Stem and Leaf StemLeaf 50 7 9 61 1 2 2 4 5 5 5 7 8 9 70 0 1 3 6 7 7 9 9 80 0 0 2 2 3 4 7 Key: 5 | 0 means 50 | 7 means 57 ( is the same value as the stem above it) 9

10. Number of rainy days in selected cities in Texas and California in a given year Texas: 6, 49, 52, 59, 63, 63, 67, 69, 71, 73, 77, 79, 79, 82, 84, 90, 96, 105 California: 29, 31, 32, 35, 35, 37, 42, 44, 45, 58, 62, 67, 75, 90, 93, 117 10

11. Stem and leaf plot StemLeaf (Texas) 06 1 2 3 49 52 9 63 3 7 9 71 3 7 9 9 82 4 90 6 105 11 Key: 0 | 6 means 6 9 | 2 means 29 11

12. Back-to-back Stem and leaf plot (California) LeafStemLeaf (Texas) 06 1 92 7 5 5 2 13 5 4 249 852 9 7 263 3 7 9 571 3 7 9 9 82 4 3 090 6 105 711 Key: 0 | 6 means 6 9 | 2 means 29 12

13. How long is a minute? 26 people were asked to estimate a duration of time – a minute in time. When they believed a minute had passed, they hit stop on their stop watch. The actual times are given below: 33, 33, 39, 42, 52, 52, 54, 55, 56, 57, 57, 59, 59, 60, 63, 64, 65, 66, 67, 68, 70, 72, 75, 79, 82, 86, 89 13

14. Stem and Leaf Plot StemLeaf 33 9 42 52 2 4 5 6 7 7 9 9 60 3 4 5 6 7 8 70 2 5 9 82 6 9 Key: 3 | 3 means 33 14

15. Histogram 15

16. Stem and Leaf Plot StemLeaf 3 3 9 4 2 5 2 2 4 5 6 7 7 9 9 6 0 3 4 5 6 7 8 7 0 2 5 9 8 2 6 9 Key: 3 | 3 means 33  | 7 means 57 ( is the same value as the stem above it) 16

17. Histogram 17

18. References About.com: Mathematics – http://math.about.com/library/weekly/aa051022a.htm Learning Math: Annenberg/CPB – http://www.learner.org.courses/learningmath/index.html University of Washington: Elementary Quantitative Literacy Program – http://faculty.washington.edu/wijsman/GRAPHS.pdf 18

19. Thank you! Dr. Cheryl Malm cgmalm@nwmissouri.edu Dr. Patricia Lucido Patricia.Lucido@Rockhurst.edu 19