1. CHAPTER 1 Picturing Distributions with Graphs BPS - 5TH ED. CHAPTER 1 1

2. STATISTICS BPS - 5TH ED. CHAPTER 1 2 Statistics is a science that involves the extraction of information from numerical data obtained during an experiment or from a sample. It involves the design of the experiment or sampling procedure, the collection and analysis of the data, and making inferences (statements) about the population based upon information in a sample.

3. INDIVIDUALS AND VARIABLES  Individuals  the objects described by a set of data  may be people, animals, or things  Variable  any characteristic of an individual  can take different values for different individuals BPS - 5TH ED. CHAPTER 1 3

4. VARIABLES  Categorical  Places an individual into one of several groups or categories  Quantitative (Numerical)  Takes numerical values for which arithmetic operations such as adding and averaging make sense BPS - 5TH ED. CHAPTER 1 4

5. DISTRIBUTION  Tells what values a variable takes and how often it takes these values  Can be a table, graph, or function BPS - 5TH ED. CHAPTER 1 5

6. DISPLAYING DISTRIBUTIONS  Categorical variables  Pie charts  Bar graphs  Quantitative variables  Histograms  Stemplots (stem-and-leaf plots) BPS - 5TH ED. CHAPTER 1 6

7. CLASS MAKE-UP ON FIRST DAY BPS - 5TH ED. CHAPTER 1 7 YearCountPercent Freshman1841.9% Sophomore1023.3% Junior614.0% Senior920.9% Total43100.1% Data Table

8. CLASS MAKE-UP ON FIRST DAY BPS - 5TH ED. CHAPTER 1 8 Pie Chart

9. CLASS MAKE-UP ON FIRST DAY BPS - 5TH ED. CHAPTER 1 9 Bar Graph

10. EXAMPLE: U.S. SOLID WASTE (2000) MaterialWeight (million tons)Percent of total Food scraps25.911.2 % Glass12.85.5 % Metals18.07.8 % Paper, paperboard86.737.4 % Plastics24.710.7 % Rubber, leather, textiles15.86.8 % Wood12.75.5 % Yard trimmings27.711.9 % Other7.53.2 % Total231.9100.0 % BPS - 5TH ED. CHAPTER 1 10 Data Table

11. EXAMPLE: U.S. SOLID WASTE (2000) BPS - 5TH ED. CHAPTER 1 11 Pie Chart

12. EXAMPLE: U.S. SOLID WASTE (2000) BPS - 5TH ED. CHAPTER 1 12 Bar Graph

13. EXAMINING THE DISTRIBUTION OF QUANTITATIVE DATA  Overall pattern of graph  Deviations from overall pattern  Shape of the data  Center of the data  Spread of the data (Variation)  Outliers BPS - 5TH ED. CHAPTER 1 13

14. SHAPE OF THE DATA  Symmetric  bell shaped  other symmetric shapes  Asymmetric  right skewed  left skewed  Unimodal, bimodal BPS - 5TH ED. CHAPTER 1 14

15. SYMMETRIC BELL-SHAPED BPS - 5TH ED. CHAPTER 1 15

16. SYMMETRIC MOUND-SHAPED BPS - 5TH ED. CHAPTER 1 16

17. SYMMETRIC UNIFORM BPS - 5TH ED. CHAPTER 1 17

18. ASYMMETRIC SKEWED TO THE LEFT BPS - 5TH ED. CHAPTER 1 18

19. ASYMMETRIC SKEWED TO THE RIGHT BPS - 5TH ED. CHAPTER 1 19

20. OUTLIERS  Extreme values that fall outside the overall pattern  May occur naturally  May occur due to error in recording  May occur due to error in measuring  Observational unit may be fundamentally different BPS - 5TH ED. CHAPTER 1 20

21. HISTOGRAMS  For quantitative variables that take many values  Divide the possible values into class intervals (we will only consider equal widths)  Count how many observations fall in each interval (may change to percents)  Draw picture representing distribution BPS - 5TH ED. CHAPTER 1 21

22. HISTOGRAMS: CLASS INTERVALS  How many intervals?  One rule is to calculate the square root of the sample size, and round up.  Size of intervals?  Divide range of data (max  min) by number of intervals desired, and round to convenient number  Pick intervals so each observation can only fall in exactly one interval (no overlap) BPS - 5TH ED. CHAPTER 1 22

23. CASE STUDY BPS - 5TH ED. CHAPTER 1 23 Weight Data Introductory Statistics class Spring, 1997 Virginia Commonwealth University

24. WEIGHT DATA BPS - 5TH ED. CHAPTER 1 24

25. WEIGHT DATA: FREQUENCY TABLE BPS - 5TH ED. CHAPTER 1 25 sqrt(53) = 7.2, or 8 intervals; range (260  100=160) / 8 = 20 = class width

26. WEIGHT DATA: HISTOGRAM BPS - 5TH ED. CHAPTER 1 26 100120140160180200220240260280 Weight * Left endpoint is included in the group, right endpoint is not. Number of students

27. STEMPLOTS (STEM-AND-LEAF PLOTS) For quantitative variables Separate each observation into a stem (first part of the number) and a leaf (the remaining part of the number) Write the stems in a vertical column; draw a vertical line to the right of the stems Write each leaf in the row to the right of its stem; order leaves if desired BPS - 5TH ED. CHAPTER 1 27

28. WEIGHT DATA BPS - 5TH ED. CHAPTER 1 28 1212

29. WEIGHT DATA: STEMPLOT (STEM & LEAF PLOT) BPS - 5TH ED. CHAPTER 1 29 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Key 20 | 3 means 203 pounds Stems = 10’s Leaves = 1’s 192 2 152 2 5 135

30. WEIGHT DATA: STEMPLOT (STEM & LEAF PLOT) BPS - 5TH ED. CHAPTER 1 30 10 0166 11 009 12 0034578 13 00359 14 08 15 00257 16 555 17 000255 18 000055567 19 245 20 3 21 025 22 0 23 24 25 26 0 Key 20 | 3 means 203 pounds Stems = 10’s Leaves = 1’s

31. EXTENDED STEM-AND-LEAF PLOTS If there are very few stems (when the data cover only a very small range of values), then we may want to create more stems by splitting the original stems. BPS - 5TH ED. CHAPTER 1 31

32. EXTENDED STEM-AND-LEAF PLOTS Example: if all of the data values were between 150 and 179, then we may choose to use the following stems: BPS - 5TH ED. CHAPTER 1 32 15 15 16 16 17 17 Leaves 0-4 would go on each upper stem (first “15”), and leaves 5-9 would go on each lower stem (second “15”).