Statistical Reasoning Discussion Paragraph next time…. Copyright © 2011 Pearson Education, Inc.

Statistical Tables and Graphs Unit 5C Statistical Tables and Graphs Copyright © 2011 Pearson Education, Inc.

Frequency Tables A basic frequency table has two columns: The first column lists the categories of data. The second column lists the frequency of each category, which is the number of times each category appears in the data set. Additional columns may include relative frequency (frequency expressed as a fraction or percentage of the total) or cumulative frequency (total of frequencies for the given category and all previous categories). Copyright © 2011 Pearson Education, Inc.

Relative and Cumulative Frequency CN (1) 1. Add to Table 5.1 columns showing the relative and cumulative frequencies. Copyright © 2011 Pearson Education, Inc.

Data Types and Binning Qualitative data describe qualities or categories. Quantitative data represent counts or measurements. When dealing with quantitative data categories, it is often useful to group, or bin, the data into categories that cover a range of possible values. Copyright © 2011 Pearson Education, Inc.

Data Types CN (2a-c) 2. Classify each of the following types of data as either qualitative or quantitative. a. Brand Names of shoes in a consumer survey b. Heights of students c. Audience ratings of a film on a scale of 1 to 5, where 5 means excellent Copyright © 2011 Pearson Education, Inc.

Summarizing Raw Data Consider the following 20 scores from a 100-point exam: 80 78 76 94 75 98 77 84 88 81 72 91 72 74 86 79 88 72 75 Determine appropriate bins and make a frequency table including columns for relative and cumulative frequency. Show students how to take raw data and do the following: 1) group data, 2) compute actual and relative frequencies, and 3) make a bar and a pie graph. Copyright © 2011 Pearson Education, Inc.

Binned Exam Scores CN (3) Consider the following set of 20 scores from a 100-point exam: 76 80 78 76 94 75 98 77 84 88 81 72 91 72 74 86 79 88 72 75 3. Determine appropriate bins and make a frequency table. Include columns for relative and cumulative frequency, and interpret the cumulative frequency for this case. Copyright © 2011 Pearson Education, Inc.

Bar and Pie Graphs A bar chart shows each category with a bar whose length corresponds to its frequency or relative frequency. Pie charts are used primarily for relative frequencies, because the total pie must always represent the total relative frequency of 100%. The size of each wedge is proportional to the relative frequency of the category it represents. Both graphs represent the same data set. Discuss the pros and cons of the graphs. Copyright © 2011 Pearson Education, Inc.

Bar and Pie Graphs The bar chart and pie chart below both show the data from table 5.1. Grade Data Both graphs represent the same data set. Discuss the pros and cons of the graphs. Grade Data Copyright © 2011 Pearson Education, Inc.

Important Labels for Graphs Title/caption: The graph should have a title or caption (or both) that explains what is being shown and, if applicable, lists the source of the data. Vertical scale and title: Numbers along the vertical axis should clearly indicate the scale. The numbers should line up with the tick marks. Include a label that describes the variable. Horizontal scale and title: The categories should be clearly indicated along the horizontal axis. (Tick marks may not be necessary for qualitative data, but should be included for quantitative data.) Include a label that describes the variable. Legend: If multiple data sets are displayed on a single graph, include a legend or key to identify the individual data sets. Copyright © 2011 Pearson Education, Inc.

Carbon Dioxide Emissions CN (4) Carbon dioxide is released into the atmosphere primarily by the combustion of fossil fuels (oil, coal, natural gas). Table 5.4 lists the eight countries that emit the most carbon dioxide each year. 4. Make bar graphs for the total emissions and the emissions per person. Put the bars in descending order of size. Copyright © 2011 Pearson Education, Inc.

Simple Pie Chart CN (5) Among registered voters in Rochester County, 25% are Democrats. 25% are Republicans, and 50% are Independents. 5. Make a pie chart showing the breakdown of party affiliations in Rochester County. Copyright © 2011 Pearson Education, Inc.

Student Majors CN (6a-b) Figure 5.7 is a pie chart showing planned major areas for first year college students. 6a. Make a bar graph showing the same data, with the bars in order of decreasing size. b. What are the three most popular major areas? Copyright © 2011 Pearson Education, Inc.

Definitions A histogram is a bar graph for quantitative data categories. The bars have a natural order and the bar widths have specific meaning. A line chart shows the data value for each category as a dot, and the dots are connected with lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the data value for the bin. A time-series diagram is a histogram or line chart in which the horizontal axis represents time. Copyright © 2011 Pearson Education, Inc.

Histogram and Line Chart The histogram and line chart below both show the same data. Both graphs represent the same data set. Discuss the pros and cons of the graphs. Copyright © 2011 Pearson Education, Inc.

Oscar-Winning Actresses CN (7a-b) Table 5.5 shows the ages (at the time when they won the award) of all Academy Award-winning actresses through 2008. 7. Make a (a) histogram and a (b) line chart to display these data. Copyright © 2011 Pearson Education, Inc.

Reading Time-Series Diagrams A time-series line chart of stock, bond, and gold prices for an initial $100 investment is shown below. If you invested $100 in bonds on July 7, how much would your investment be worth on August 25? About $97.50 Copyright © 2011 Pearson Education, Inc.

Reading a Time-Series Diagram CN (8) Suppose that on July 7, you invested $100 in a stock fund that tracks the S&P 500, $100 in a bond fund that follows the Treasury Bond Index, and $100 in gold. If you sold all three funds on August 4, How much did you gain or lose? Copyright © 2011 Pearson Education, Inc.

Quick Quiz p.331 CN (9) Answer questions 1-10 together as a class, put down the multiple choice answer on your class notes for each question. Copyright © 2011 Pearson Education, Inc.

5C Homework P.332: 1-14 1 web 1 World Class Notes 1-9 48. CO2 Emissions 49. Energy Table 50. Statistical Abstract 1 World 51. Frequency Tables 52. Bar Graph 53. Pie Chart 54. Histogram 55. Line Chart Class Notes 1-9 Copyright © 2011 Pearson Education, Inc.