1. Displaying Categorical Variables Frequency Table 1Section 2.1, Page 24 Variable Categories of the Variable Count of elements from sample in each category. Total = 498

2. Displaying Categorical Variables Relative Frequency Circle Graph 2Section 2.1, Page 25 Relative Frequency or Proportion. 74/498 = 15%

3. Displaying Categorical Variables Vertical Bar Graph 3Section 2.1, Page 25

4. Displaying Categorical Variables Pareto Chart for Hate Crimes USA 1993 4Section 2.1, Page 25 Cumulative count/relative frequency Frequency, Relative Frequency, and Cumulative Relative Frequency Table

5. Displaying Quantitative Data Dot Plots 5Section 2.2, Page 26

6. Displaying Quantitative Data Stem-and-Leaf Displays To make stem-and-leaf display, first find the minimum and maximum number, 52 and 96. We then graph the tens digits in the left column, 5 – 9. We then plot each number opposite its tens digit. The plot point is the ones digit. 6Section 2.2, Page 27

7. Stem-and Leaf-Displays Problems 7Problems, Page 50

8. Displaying Quantitative Data Ungrouped Frequency Distribution 8Section 2.1, Page 29 Values of the Variable in the data set Frequency or number of times each value occurs in the data set

9. Displaying Quantitative Data Grouped Frequency Distribution 9Section 2.2, Page 30 Classes or bins, usually 5 to 12 of equal width 95 or more to less than 105

10. Displaying Quantitative Data Histograms Histogram: A bar graph that represents a frequency distribution of a quantitative variable. 10Section 2.2, Page 32 5 to 12 equal sized classes or bins 5 10 15 Count

11. Histograms Shapes of Distributions 11Section 2.2, Page 33

12. Calculator Fundamentals Clear the Home screen: “Clear” key Setting the calculator decimal places: “Mode” key: Down arrow key to “FLOAT”, right arrow key to desired number, then “ENTER” Entering data into a List: “STAT-Edit- Enter”: Type in each number followed by “ENTER” or down arrow. Deleting number for a list: Position the cursor over the number and press “Del” key. Clear a List: Position the cursor over the list title, press “Clear-Enter”. Caution if you press “DEL” you will eliminate the entire list position. Return to Home Screen: “2 nd – Quit Scientific Notation: When an answer will be less than 1 with more than three zeros after the decimal point, the calculator will return the answer in Scientific Notation. For example, the number 5.3E-5 is converted to normal notation by moving the decimal point 5 places left: 0.000053. 12Section 2.2

13. Constructing Histogram TI-83 Calculator Enter Data: STAT-1:Edit-ENTER Type all the data in L1 Set up Plot: 2 nd Stat Plot Enter --Turn plot ON, select Histogram Icon, enter XList: as L1 and Freq: as 1 Set the Viewing Window Zoom 9: ZoomStat – Hit Trace key then arrows to view axes values. Change category size to 7 Window –Make Xscl= 7. Then hit Graph Key Display class width and frequency. Trace (50 States) 13Section 2.2

14. TI-83 Histogram Display # of States % College Students Enrolled in Public Institutions The leftmost class or bin shows the number of states between 44 and <51. There are 2 states in this bin. To see the next bin, hit the right arrow button. 14Section 2.2 WS #21

15. Histogram Problem 2.4 Heights of NBA players selected in the June 2004 Draft. a.Construct a histogram. Be sure to show the scale and the label for the x and y axes. b.Describe the shape of the distribution. 15Section 2.2, Page 50

16. Cumulative Frequency Distribution Final Exam Scores for 50 Students For classes <65, 11/50 =.22 16Section 2.2, Page 34 Cumulative Relative Frequency 2/50 =.04 4/50 =.08 11/50 =.22 24/50 =.48 35/50 =.70 46/50 =.92 50/50 = 1.0 Cumulative Relative Frequency

17. Measures of Central Tendency Mean Find the sample mean for the set {6, 3, 8, 6, 4} 17Section 2.3, Page 35

18. Measures of Central Tendency Median The median is the value of the middle number when the data are ranked according to size. Find the median for the data the following set with an odd n: {3, 3, 5, 6, 8}, n=5. The data values are in ascending order. Depth of median = (n+1)/2. For this set: (5+1)/2 = 3 The median is the 3 rd number, 5. Find the median for the following data values that are in ascending order with even n: {6, 7, 8, 9, 9, 10}, n=6. Dept of median = (n+1)/2 = 3.5 The median is then the average of the 3 rd and 4 th number. The median is (8+9)/2 = 8.5 18Section 2.3, Page 36

19. Measures of Central Tendency Mode and Midrange 19Section 2.3, Page 37 (L+H)/2 = (3+8)/2 = 5.5

20. Measures of Central Tendency Summary The most useful measure is the mean. However, when a set of numbers has outliers, the mean gets distorted and may not be representative of the central tendency. When this happens, the median is a better measure of central tendency because it is not affected by outliers. 20Section 2.3, Page 37

21. Measures of Dispersion Range 21Secton 2.4, Page 39

22. Measures of Dispersion Variance and Standard Deviation 22Section 2.4, Page 41 {6, 3, 8, 5, 3 }

23. Measures of Position Percentiles Percentiles: Values of the variable that divide a set of ranked data into 100 equal subsets: each set of data has 99 percentiles. A specific number from within the range of values In the set 23Section 2.5, Page 42

24. Finding Percentiles Example Find the 21 st Percentile. Sample size n=20. Calculate the depth: percentile*n/100 = 21*20/100 = 4.2. (If the depth is an integer, P k is the average of the number and the next number. If the depth contains a decimal, P k is the next number.) Since the depth contains a decimal, P k is the next number, the 5 th number, P k = 23. Find the 75 th Percentile: Depth = 75*20/100 = 15. Since the depth is an integer, the 75 th percentile is the average of the 15 th and 16 th numbers, (79+82)/2=80.5. Sample data set of 20 numbers in ascending rank order: {6, 12, 14, 17, 23, 27, 29, 33, 42, 51, 59, 65, 69, 74, 79, 82, 84, 88, 92, 97} 24Section 2.5, Page 43

25. Using the TI-83 to Find Percentiles Find the 21 st and the 75 th percentile of the following data set. {6, 12, 14, 17, 23, 27, 29, 33, 42, 51, 59, 65, 69, 74, 79, 82, 84, 88, 92, 97} STAT-EDIT: Enter the data in L1 PRGM: down arrow to PRCNTILE ENTER: (Copies program to home screen) ENTER: (Displays Program Input Page) 2 nd L1: (Enters the List name) ENTER: (Asks for Percentile) 21.0: (Enters the desired percentile) ENTER: (Displays the 21 st percentile) ENTER-2 ND L1-75: (Displays the 75 th percentile) CLEAR: (Clears the home screen) 25Section 2.5, Page 43

26. 5-Number Summary Box and Whisker Display L Q1Q1 Q3Q3 H Med 26Section 2.5, Page 44 Interquartile Range = Q 3 -Q 1 Range of middle 50% of values Measure of dispersion resistant to outliers.

27. TI – 83 Problem (1) a.Find the mean, standard deviation sample data. STAT – EDIT: Enter the data is L1 PRGM – SAMPSTAT - ENTER 2 ND L1 - ENTER DISPLAY: Sample Mean 27Problems, Page 52 Standard Deviation Variance

28. TI-83 Problem (2) b.Find the Interquartile range (IQR) Q3 – Q1 = 32 – 28 = 4 c.Find the range. Max – Min = 34 – 25 = 9 28Problems, Page 50

29. TI-83 Problem (3) d.Make a box and whisker display of the data. 2 ND STAT PLOT-ENTER ENTER: Sets plot to ON DOWN ARROW RIGHT ARROW 5 TIMES: Select box Plot DOWN ARROW – 2 nd L1: Select List Display: ZOOM – 9 TRACE: Display: RIGHT-LEFT ARROW: Display 5-number summary 29Problems, Page 50

30. Summary: Measures of Center and Spread The mean and median are measures of the center of a distribution. Outliers will distort the mean, so when outliers are present the mean is not a good measure of the center. The median is not distorted by outliers. The standard deviation, variance, range, and Interquartile range (IQR) are measures of the spread or variability of a distribution. Outliers will distort the standard deviation, variance, and range, so when outliers are present, these are not good measures of the spread or variability. The Interquartile range is not distorted by outliers. When outliers are present, then use the median and IQR as measures of the center and spread. When no significant outliers are present, use the mean and standard deviation as measures of center and spread. These measures allow use of the maximum number statistical tools using the distribution. 30Section 2.4

31. Problem a.Find the mean, variance, and standard deviation. b.Find the 5-number summary. c.Make a box and whisker display and label the numbers. d.Calculate the Interquartile range and the range e.Describe the shape of the distribution f.Find the 33 rd percentile. 31Problems, Page 50

32. Problem a.Find the mean, variance, and standard deviation. b.Find the 5-number summary. c.Make a box and whisker display and label the numbers. d.Calculate the Interquartile range and the range e.Describe the shape of the distribution. f.Find the 90 th percentile. 32Problems, Page 50