1. Frequency Distributions and Graphs

2. Where do we start? Quantitative Data is a set that can be numerically represented.

3. Dealing With a Lot of Numbers... When looking at large sets of quantitative data, it can be difficult to get a sense of what the numbers are telling us without summarizing the numbers in some way.

4. What do these data tell us? Make a table –Frequency Distribution Make a picture –Histogram –Stem-and-Leaf Display Describe the distribution –Shape, center, spread, outliers

5. Frequency Distribution Chart or table with 3 required columns: 1.Classes (# given) Width = 2.Frequency 3.Cumulative Frequency

6. Example The data shown (in millions of dollars) are the values of the 30 NFL franchises. What can you tell me about this data by looking at the raw data? 170191171235173187181191 200218243200182320184239 186199186210209240204193 211186197204188242

7. Frequency Distribution (8 Classes) Start by sorting the data Class width = (max – min)/(# of classes) = (320 – 170) / 8 = 150 / 8 = 18.75 ≈ 19

8. Frequency Distribution (8 Classes) NFL Team Values ClassesFrequencyCumulative Frequency 170 – 18811 189 – 207920 208 – 226424 227 – 245529 246 – 264029 265 – 283029 284 – 302029 303 - 321130

9. Histogram NFL Team Values Class BoundariesClassesFrequencyCumulative Frequency 169.5 – 188.5170 – 18811 188.5 – 207.5189 – 207920 207.5 – 226.5208 – 226424 226.5 – 245.5227 – 245529 245.5 – 264.5246 – 264029 264.5 – 283.5265 – 283029 283.5 – 302.5284 – 302029 302.5 – 321.5303 - 321130 To make a histogram add and subtract 0.5 from either end of the classes.

10. Histogram To make a histogram put boundaries on x-axis and frequencies on y-axis.

11. Displaying Quantitative Data Stem and Leaf Display –Leaf Contains the last digit of the values Arranged in increasing order away from stem –Stem Contains the rest of the values Arranged in increasing order from top to bottom

12. Example – Spurs Last 20 scores of regular season games (’05/’06). 89115 103 80 104 83 86 87 95 106 96 98 102 98 92 107 92 108 96 88 8036789 92256688 10234678 115

13. Displaying Quantitative Data Back-to-back Stem-and-Leaf Display –Used to compare two variables –Stems in center column –Leafs for one variable – right side –Leafs for other variable – left side –Arrange leafs in increasing order, AWAY FROM STEM!

14. Example – Compare Spurs to Pistons Last 20 scores of Pistons regular season games. 80 93 103 103 96 98 87 95 101 109 112 101 97 74 75 82 91 108 103 105 547 72080367899 87653192256688 9853331110234678 2115

15. Looking at Distributions Always report 4 things when describing a distribution: 1.Shape 2.Center 3.Spread 4.Outliers

16. Looking at Distributions Shape –How many humps (called modes)? None = uniform One = unimodal Two = bimodal Three or more = multimodal

17. Looking at Distributions Shape –Is it symmetric? Symmetric = roughly equal on both sides Skewed = more values on one side –Right = Tail stretches to large values –Left = Tail stretches to small values

18. Looking at Distributions Center –A single number to describe the data –Can calculate different numbers for center –For this chapter, just EYE BALL IT – we will learn numerical descriptions next chapter

19. Looking at Distributions Spread –Variation in the data values Crude measure: Range = max. value – min. value Again, next chapter spread will be a single number Outliers? –Interesting observations in data Can impact statistical methods

20. 65 & Over Histogram 2000 Census Pop Over 65 Frequency 4681012141618 0 5 10 15 20 25

21. Displaying Categorical Data

22. Categorical Data Categorical variables are variables that cannot be measured numerically –Examples Gender Religion Colors Race Occupation Emotions

23. Describing Categorical Data Pie Charts Bar Charts

24. Pie Chart Displays percentage of whole (for each category) Must include all possible categories

25. Example of Pie Chart 2004 Enrollment Iowa State University –Agriculture 12% –Business 17% –Design 8% –Education 7% –Engineering 22% –F&C Sciences 6% –Liberal Arts 28%

26. Bar Charts Displays either number or percentage for each category Do not need to include all possible categories

27. Example of a Bar Chart Number of students from Iowa and beyond –Iowa: 16424 –Non-Iowa U.S.: 4157 –Foreign: 741