1. Section 4-1 Graphs, Good and Bad
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2. Statistics is the science of planning studies and experiments
obtaining data
organizing, summarizing, presenting, analyzing, and interpreting data
drawing conclusions based on the data
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3. Data
collections of observations (such as measurements, genders, survey responses)
Review
Two types of Data –
1. Categorical
2. Quantitative (or Numeric)
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4. Categorical (qualitative) Data
consists of names or labels (representing categories)
Example: The genders (male/female) of professional athletes
Example: Shirt numbers on professional athletes uniforms - substitutes for names.
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5. Where Does the Information Come From?
A question is asked.
What kind of ice cream does
everyone like in our class?
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6. How Is the Information Gathered?
A survey is made.
Chocolate
Vanilla
111
Strawberry
1111
Mint & Chip
Rocky Road 11
Bubble Gum 1
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7. How Is the Information Presented?
Pie chart is made to describe the data.
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8. How Is the Information Presented?
A bar graph is made to display the data.
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9. Bar Graph
Uses bars of equal width to show frequencies of categories of qualitative data.
Vertical scale represents frequencies or relative frequencies.
Horizontal scale identifies the different categories of qualitative data.
A multiple bar graph has two or more sets of bars, and is used to compare two or more data sets.
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10. Median Income of Males and Females
Multiple Bar Graph
Median Income of Males and Females
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11. “Stacked” Bar Graphs
Another way to merge bar graphs is to “stack” all the bars of an ordinary bar graph on top of one another to form a single bar representing 100% of the (valid) cases.
We can then combine nine such stacked bars to “tell the story” of the changing perceived importance of different types of issues in Presidential elections over the last 33 years.
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13. Bar graphs, unlike pie charts, CAN add to more (or less) than 100%.
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14. Line Graph Never use line graphs to display qualitative (categorical) data ….only use pie charts or bar graphs
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15. Bad Graphs Some graphs are bad in the sense that they contain errors.
Some are bad because they are technically correct…but misleading.
Some are simply too complicated to understand!!!
It is important to develop the ability to recognize bad graphs and identify exactly how they are misleading.
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16. But pie charts are not helpful if there are many unordered categories
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17. Nonzero Axis
Misleading because one or both of the axes begin at some value other than zero, so that differences are exaggerated.
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18. Pictographs Drawings of objects.
Example: three-dimensional objects such as money bags, stacks of coins, army tanks (for army expenditures), people (for population sizes), barrels (for oil production), and houses (for home construction) are commonly used to depict data.
These drawings can create false impressions that distort the data.
Pictographs using areas and volumes can therefore be very misleading.
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19. Annual Incomes of Groups with Different Education Levels
Bars need to have the same width
This is too busy, too difficult to interpret and understand.
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20. Annual Incomes of Groups with Different Education Levels
Misleading because it depicts one-dimensional data with three-dimensional boxes. Last box is 64 times as large as first box, but income is only 4 times as large.
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21. Annual Incomes of Groups with Different Education Levels
Fair, objective, unencumbered by distracting features.
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22. Graphs
To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the shape of the graph. READ labels and units on the axes!
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23. Pictographs
Diagram b is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption.
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