1. Organizing and Graphing Qualitative Data https://www.youtube.com/watch?v=BhMKmovNjvc

2. Frequency Distributions Raw Data – data recorded in the sequence in which they are collected before they are processed or ranked We survey 100 college students about their plans after graduating. 44 want to work for private companies, 16 want to work for the federal government, 23 want to work for state or local government, and 17 want to start their own business.

3. Frequency Distributions We create a table to list the different categories of employment and the number of students that belong to that category. Type of EmploymentNumber of Students Private Companies44 Federal Government16 State/Local Government23 Own business17 Sum = 100 Variable Category Frequency

4. Definition Frequency Distribution – lists all categories and the number of elements that belong to each of the categories.

5. A sample of 30 employees asked how stressful their jobs were. somewhat nonesomewhatveryverynone verysomewhatsomewhatverysomewhatsomewhat verysomewhat noneverynonesomewhat somewhatverysomewhatsomewhat very none somewhatveryverysomewhatnonesomewhat

6. The variable in this example is the question, “How stressful is an employee’s job.” The variable is classified into 3 categories: very stressful, somewhat stressful, not stressful We list the 3 categories in the first column then start counting and marking a tally.

7. Frequency Distribution of Stress on Job Stress on JobTallyFrequency (f) Very|||| 10 Somewhat|||| |||| ||||14 None|||| |6 Sum = 30

8. Relative Frequency and Percentage Distributions

9. Calculating the percentage Percentage for a category is obtained by multiplying the relative frequency of that category by 100 If the relative frequency of “none” is.200, then the percentage is (.200)(100) or 20%

10. Stress on JobRelative FrequencyPercentage very10/30 =.333.333(100) = 33.3 somewhat14/30 =.467.467(100) = 46.7 none 6/30 =.200.200(100) = 20.0 Sum = 1.000 Sum = 100 Relative Frequency and Percentage Distributions of Stress on Job **Note: sum of the relative frequency should always equal 1 (or about 1 depending on rounding) and the sum of percentages should always equal 100 (or about 100 depending on rounding)

11. Graphical Presentation of Qualitative Data Bar Graphs Graph made of bars whose heights represent the frequencies of respective categories Mark all of the various categories on the x-axis (very, somewhat, none) Frequencies marked along the y-axis Leave small gap between bars

12. Pie Charts Circle divided into portions that represent the relative frequencies or percentages of a population or sample belonging to different categories More commonly used for displaying percentage data Use relative frequency or percentage to find degree measure or angle size for each category

14. The following data give the results of a sample survey. The letters A, B, and C represent the three categories. ABBACBCCCA CBCACCBCCA ABCCBCBACA a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories c. What percentage of the elements in this sample belong to category B? d. What percentage of the elements in this sample belong to category C? e. Draw a bar graph for the frequency distribution. f. Draw a pie chart for the percentage distribution.

15. Organizing and Graphing Quantitative Data

17. Frequency Distribution Table Weekly Earnings (dollars) Number of Employees f 401 to 6009 601 to 80022 801 to 100039 1001 to 120015 1201 to 14009 1401 to 16006 Weekly Earnings of 100 Employees of a Company Variable Third class Lower limit of 6 th class Upper limit of 6 th class Frequency of third class

18. Organizing and Graphing Quantitative Data Frequency distribution for quantitative data – lists all the classes and the number of values that belong to each class. Class – the interval in quantitative data that includes all the values that fall within 2 numbers, the lower and upper limits. Lower limits are the smallest number in each class Upper limits are the largest numbers in each class

19. Number of classes Although 5 to 20 classes in a frequency distribution is standard, there are no set rules as to how many classes there should be. It is up to the data organizer. What should you look for? Class Width It is preferred to have classes the same width. Why? To find: (Largest Value – Smallest Value) / Number of classes; then round if needed Starting point – lower limit of the first class Any convenient number equal to or less than the smallest value in the data set.

20. Construct a frequency distribution table for quantitative data Start with some data, let’s use Number of home runs hit by MLB teams during 2004 season TeamHome RunsTeamHome RunsTeamHome RunsTeamHome RunsTeamHome Runs Arizona135Cincinnati194Kansas City150New York Mets 185San Diego139 Atlanta178Cleveland184Anaheim Angels162New York Yankees 242San Francisco183 Baltimore169Colorado202Los Angeles Dodgers 203Oakland189Seattle136 Boston222Detroit201Milwaukee135Philadelphia215Tampa Bay145 Chicago Cubs235Florida148Minnesota191Pittsburgh142Texas227 Chicago White Sox 242Houston187Montreal151St Louis214Toronto145

21. The largest value is 242, smallest is135. Lets try 5 classes, so (242-135)/5 = 21.4 round up, and the width of each class should be 22. Starting with the smallest value and increasing by 22, we come up with the following class limits: 135-156, 157-178, 179-200, 201-222, and 223-244 Could we start with something less than 135 as our starting point?

22. Our table starts to look like this Total Home RunsTallyf 135-156 157-178 179-200 201-222 223-244 Now tally up the number of home runs in each class

23. Tallying the numbers Total Home RunsTallyf 135-156|||| 157-178||| 179-200|||| || 201-222|||| | 223-244|||| Now the frequency numbers

24. Adding Frequency numbers Total Home RunsTallyf 135-156|||| 10 157-178|||3 179-200|||| ||7 201-222|||| |6 223-244||||4 Σf=30 What do we lose when collecting data this way? Now calculate relative frequency and percentage distribution like with the qualitative data.

25. Adding Relative Frequency and Percentage Distribution Total Home RunsTallyfRelative FrequencyPercentage 135-156|||| 1010/30 =.33333.3 157-178|||33/30 =.10010.0 179-200|||| ||77/30 =.23323.3 201-222|||| |66/30 =.20020.0 223-244||||44/30 =.13313.3 Σf=30Sum =.999Sum = 99.9%

26. What does our table start to tell us? Total Home RunsTallyfRelative FrequencyPercentage 135-156|||| 1010/30 =.33333.3 157-178|||33/30 =.10010.0 179-200|||| ||77/30 =.23323.3 201-222|||| |66/30 =.20020.0 223-244||||44/30 =.13313.3 Σf=30Sum =.999Sum = 99.9%

27. Histograms Histograms used for grouped data (our homerun data) Can use frequency, relative frequency, or percentage distribution Mark the classes along the x-axis Mark frequencies (or rel. freq. or percentages) along the y-axis Drawn like a bar graph, with the exception the bars are adjacent: no gaps

29. Shapes of Histograms Symmetric Skewed Uniform or rectangular

30. Symmetric Identical on both sides of its central point

31. Skewed the tail on one side is longer than the other Skewed to the rightSkewed to the left

32. Uniform or rectangular

33. Using graphs is both helpful and deceiving

35. “Picture is worth a thousand words” 2 ways to manipulate a graph to convey a particular opinion Changing the scale Truncating the frequency table

36. Cumulative Frequency Total Home RunsTallyfRelative FrequencyCumulative Frequency 135-156|||| 1010/30 =.333.333 157-178|||33/30 =.100.433 179-200|||| ||77/30 =.233.666 201-222|||| |66/30 =.200.866 223-244||||44/30 =.133.999 Σf=30Sum =.999

37. Cumulative Percentage Total Home RunsRelative FrequencyCumulative FrequencyPercentageCumulative Frequency 135-15610/30 =.333.33333.3% 157-1783/30 =.100.43310.0%43.3% 179-2007/30 =.233.66623.3%66.6% 201-2226/30 =.200.86620.0%86.6% 223-2444/30 =.133.99913.3%99.9% Sum =.999 Sum = 99.9%