1. Statistics Part 10

2. Representing Data We can use many different ways to represent data. Some of these ways include, but are not limited to: Tables Charts Pie graphs Histograms Bar graphs

3. Frequency Tables Frequency tables frequently bin data into small groups. We use a table to show this with columns for the data category, frequency, relative frequency, and cumulative frequency. Frequency is how often values in that bin occurred. Relative frequency is how often out of the total values in that bin occur. (Related to probability.) Cumulative frequency is the total number of values thus far in the table.

4. Example 1: Exam Grades On a certain exam, students scored exam grades of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67, 67, 67, and 62. Use 5-point bins to make a frequency table for the exam scores. Exam ScoresNumber of StudentsRelative FrequencyCumulative Frequency 95 - 10033/15 = 0.2 = 20%3 90 - 9411/15 = 0.067 = 6.7%3 + 1 = 4 85 - 8933/15 = 0.2 = 20%3+1+3 = 7 80 - 8411/15 = 0.067 = 6.7%3 + 1 + 3 + 1 = 8 75 - 7911/15 = 0.067 = 6.7%8 + 1 = 9 70 - 7422/15 = 0.133 = 13.3%9 + 2 = 11 65 - 6933/15 = 0.2 = 20%11 + 3 = 14 60 - 6411/15 = 0.067 = 6.7%14 + 1 = 15 Totals1515/15 = 100%15

5. Example 2: Exam Grades (Again) On a certain exam, students scored exam grades of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67, 67, 67, and 62. This time, use 10-point bins to make a frequency table for the exam scores. Exam ScoresNumber of StudentsRelative FrequencyCumulative Frequency 90 - 10044/15 = 0.267 = 26.7%4 80 - 8944/15 = 0.267 = 26.7%4 + 4 = 8 70 - 7933/15 = 0.2 = 20%4 + 4 + 3 = 11 60 - 6944/15 = 0.267 = 26.7%4 + 4 + 3 + 4 = 15 Totals1515/15 = 100%15

6. Histograms A histogram is a bar chart for quantitative data. The bars have a natural order and the bar widths have specific meaning. Review each example and construct the histograms to match.

7. Example 1: Exam Grades On a certain exam, students scored exam grades of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67, 67, 67, and 62. Use 5-point bins to make a frequency table for the exam scores. Exam ScoresNumber of StudentsRelative FrequencyCumulative Frequency 95 - 10033/15 = 0.2 = 20%3 90 - 9411/15 = 0.067 = 6.7%3 + 1 = 4 85 - 8933/15 = 0.2 = 20%3+1+3 = 7 80 - 8411/15 = 0.067 = 6.7%3 + 1 + 3 + 1 = 8 75 - 7911/15 = 0.067 = 6.7%8 + 1 = 9 70 - 7422/15 = 0.133 = 13.3%9 + 2 = 11 65 - 6933/15 = 0.2 = 20%11 + 3 = 14 60 - 6411/15 = 0.067 = 6.7%14 + 1 = 15 Totals1515/15 = 100%15

8. Example 2: Exam Grades (Again) On a certain exam, students scored exam grades of 98, 96, 96, 93, 87, 87, 85, 84, 76, 74, 72, 67, 67, 67, and 62. This time, use 10-point bins to make a frequency table for the exam scores. Exam ScoresNumber of StudentsRelative FrequencyCumulative Frequency 90 - 10044/15 = 0.267 = 26.7%4 80 - 8944/15 = 0.267 = 26.7%4 + 4 = 8 70 - 7933/15 = 0.2 = 20%4 + 4 + 3 = 11 60 - 6944/15 = 0.267 = 26.7%4 + 4 + 3 + 4 = 15 Totals1515/15 = 100%15

9. Bar Charts Bar charts look a lot like histograms but the bars are not touching. The width of each bar has no real meaning. We use these for comparisons of data.

10. Example 3: Local Weather The weekend forecast for Las Cruces, NM indicates the following: Friday 80/58 Saturday 78/55 Sunday 80/57 The weekend forecast for Coeur d’Alene, ID indicates the following: Friday 74/46 Saturday 73/49 Sunday 64/44 Construct a bar chart comparing the high temperatures for the weekend in these two cities.

11. Believing Statistical Studies 1.Identify the goal, population, and type of study. 2.Consider the source. 3.Consider potential bias. 4.Look for problems in defining or measuring the variables of interest. 5.Look for other variables that may confound (confuse) the data. 6.Consider the setting and wording in the survey.