1. Graphing Data

2.  Frequency Distributions DVFreq. 12 24 310 425 536 618 77 82 91

3. Graphing Data  Frequency Distributions Each value of interest listed on the x-axis Best suited when variable has small, finite number of possible values  What types of variables fit this definition?

4. Graphing Data  Stem-and-Leaf Displays Raw DataStemLeaf 0 1 1 2 2 3 4 4 4 5 5 5 6 6 7 7 7 7 8 8 9 0 0112234445556677778899 10 11 11 11 12 12 12 13 13 13 13 13 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 18 18 18 18 19 19 1 0111222333334445555556666 666666777888899 20 20 21 21 22 22 23 23 24 24 24 24 25 25 26 26 27 28 28 29 2 00112233444455667889 30 30 35 3 005

5. Graphing Data  Stem and leaf displays “Stem” = “Leading Digit” = “Most Significant Digit” “Leaf” = “Trailing Digit” = “Least Significant Digit” Unlike frequency distribution, can reconstruct entire raw data set very easily Stem is typically tens digit (Xx), but can be hundreds (Xxx) if all values are 100+ or the thousands (Xxxx) if all values are 1,000+ Bad if we have many of our values under one stem

6. Graphing Data  Stem-and-Leaf Displays

7. Graphing Data  Stem-and-Leaf Displays BDI2TOT Stem-and-Leaf Plot Frequency Stem & Leaf 28.00 0 * 0000000000000000111111111111 25.00 0 t 2222222222223333333333333 23.00 0 f 44444444444455555555555 30.00 0 s 666666666666666666777777777777 22.00 0. 8888888888899999999999 17.00 1 * 00000001111111111 18.00 1 t 222222222223333333 14.00 1 f 44444444555555 9.00 1 s 666667777 18.00 1. 888888889999999999 6.00 2 * 000111 2.00 2 t 33 6.00 2 f 445555 4.00 2 s 6677 2.00 2. 88 1.00 3 * 1 2.00 3 t 22 11.00 Extremes (>=35) Stem width: 10 Each leaf: 1 case

8. Graphing Data  Put the following data in a stem and leaf plot using the *, t, f, s,. system 0 1 1 2 2 3 4 4 4 5 5 5 6 6 7 7 7 7 8 8 9 10 11 11 11 12 12 12 13 13 13 13 13 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 18 18 18 18 19 19 20 20 21 21 22 22 23 23 24 24 24 24 25 25 26 26 27 28 28 29 30 30 35

9. Graphing Data  Histograms Bars represent certain interval – in this case 10 units  1 st bar = 0-10, 2 nd bar = 11-20, etc.  Best for data that fall into intervals naturally, i.e. discrete, categorical, nominal or sometimes ordinal variables

10. Graphing Data  Histograms When choosing graph intervals, only rule is to maximize quick readability Outlier

11. Graphing Data  Histograms 2 nd bar = 11-20 In practice though, a score of 10.5 would be rounded to 11, and a score of 20.4 to 20, and so our actual range is from 10.5 – 20.4  these are called the real upper limits and the real lower limits 11-20 = upper and lower limits 10.5-20.4 = real upper and lower limits What are the real limits for our 3 rd bar (21-30)?

12. Graphing Data  Line Graphs Best for when data continuous, dimensional, or on interval or ratio scales Same as previous histogram, but provides much richer information  if this information is meaningful, use a line graph – if it’s just noise, use a bar graph

13. Graphing Data

15.  Ways to Describe a Graph: Symmetry Modality Skewness Kurtosis

16. Graphing Data  Ways to Described a Graph: Symmetry (the graph below is Symmetric)

17. Graphing Data  Ways to Described a Graph: Modality (the graph below is Bimodal)

18. Graphing Data  Ways to Described a Graph: Skewness (the graph below is Right/Positively Skewed, and hence Non-symmetric)

19. Graphing Data  Ways to Described a Graph: Kurtosis

20. Graphing Data  Ways to Described a Graph: Kurtosis

21. Graphing Data  Ways to Described a Graph: Kurtosis