2. Statistical Reasoning Discussion Paragraph next time….
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3. Statistical Tables and Graphs
Unit 5C
Statistical Tables and Graphs
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4. 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).
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5. Relative and Cumulative Frequency CN (1)
1. Add to Table 5.1 columns showing the relative and cumulative frequencies.
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6. 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.
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7. 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
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8. Summarizing Raw Data
Consider the following 20 scores from a 100-point exam:
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.
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9. Binned Exam Scores CN (3)
Consider the following set of 20 scores from a 100-point exam:
3. Determine appropriate bins and make a frequency table. Include columns for relative and cumulative frequency, and interpret the cumulative frequency for this case.
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10. 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.
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11. 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
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12. 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.
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13. 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.
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14. 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.
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15. 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?
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16. 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.
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17. 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.
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18. 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.
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19. 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
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20. 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?
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21. 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.
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22. 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
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