1. Graphing Data

2. Graphing Data • Frequency Distributions

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

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

9. Graphing Data • Histograms • Bars represent certain interval – in this case 10 units • 1st bar = 0-10, 2nd 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 • 2nd 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 3rd 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

14. Graphing Data

15. Graphing Data • 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