2. Statistical Reasoning
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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. 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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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. Making a Histogram using Excel 2010
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13. 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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14. Quantitative Problem Solving Textbook
Read over the Aquarium problem on page 55
Look at the picture of the aquarium
Look at the time history of the chart’s water level
Be prepared to discuss the events A – J, and
Answer question K
Read over Let’s Get Graphic on pages 65 – 66
Be prepared to discuss A, B, C, and D
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15. Unit 5D
Graphics in the Media
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16. Graphics Beyond the Basics
A multiple bar graph has two or more sets of bars that allow comparison between two or more data sets. All the data sets must involve the same categories so that they can be displayed on the same graph.
A stack plot shows different data sets in a vertical stack. Stack plots usually use either stacked bars or stacked line graphs.
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17. A Multiple Bar Graph
The following multiple bar graph shows how education affects personal employment.
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18. A Stack Plot
The following stack plot shows trends in death rates from four diseases.
Illustrate with this graphic how color can help the researcher identify, at a glance, patterns and key geographical regions that may be of an influence in the context of the study.
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19. Reading a Stack Plot What was the death rate for tuberculosis in 1930?
About 220 – 100 = 120 deaths per 100,000
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20. A Few Cautions about Graphics
Perceptual distortions: Many graphics are drawn in a way that distorts our perception of them.
Watch the scales: It can be visually deceptive if you do not study the scales carefully.
Percentage change graphs: Graphs that show percentage change can be misleading unless you interpret them with great care.
Pictographs: Pictographs are graphs embellished with additional artwork. The artwork may make the graph more appealing, but can also mislead.
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21. Perceptual Distortion
The lengths of the dollars to the right represent the data, but your eyes tend to focus on the area.
Show students why many two-dimensional graphics can distort our perspective either intentionally or unintentionally. Explain the idea of area versus length of the dollars.
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22. Different Vertical Scales
Illustrate and stress the importance of choosing a scale when graphing data and reading a graph's scale carefully. Help students realize that the choice of a scale can change the look of the data.
Both graphs show the same data, but they look very different because their vertical scales have different ranges.
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23. Different Horizontal Scales
Illustrate and stress the importance of choosing a scale when graphing data and reading a graph's scale carefully. Help students realize that the choice of a scale can change the look of the data.
It appears that the world population has been rising linearly. However, the time intervals on the horizontal axis are not uniform in size.
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