1. Section 2-4
Statistical Graphics

2. Key Concept This section discusses other types of statistical graphs.
Our objective is to identify a suitable graph for representing the data set. The graph should be effective in revealing the important characteristics of the data.

3. Frequency Polygon
Uses line segments connected to points directly above class midpoint values

4. Example 1: Use the weights of discarded plastic in the table below to construct a frequency polygon. For the horizontal axis, use the lower class limits of these class intervals:
0.00 – 0.99, 1.00 – 1.99, 2.00 – 2.99, 3.00 – 3.99, 4.00 – 4.99, 5.00 – 5.99.
0.27
1.41
2.19
2.83
1.81
0.85
3.05
3.42
2.10
2.93
2.44
2.17
2.00
0.93
2.97
2.04
0.65
2.13
0.63
1.53
4.69
0.15
1.45
2.68
3.53
1.49
2.31
0.92
0.83
0.80
0.72
2.66
4.37
1.40
1.68
1.44
1.36
0.38
1.74
2.35
2.30
1.14
2.88
5.28
1.48
3.36
2.87
2.96
1.61
1.58
1.15
1.28
0.58
0.74
Weights (lbs) of
Discarded Plastic
Frequency
0.00 – 0.99
1.00 – 1.99
2.00 – 2.99
3.00 – 3.99
4.00 – 4.99
5.00 – 5.99

6. Relative Frequency Polygon
Uses relative frequencies (proportions or percentages) for the vertical scale.

7. Weights (pounds) of discard plastic
Example 2: Use the weights of discarded plastic in the frequency distribution below to construct a relative frequency polygon. For the horizontal axis, use the lower class limits of these class intervals:
0.00 – 0.99, 1.00 – 1.99, 2.00 – 2.99, 3.00 – 3.99, 4.00 – 4.99, – 5.99.
Weights (pounds) of discard plastic
Frequency
0.00 – 0.99 14
1.00 – 1.99 20
2.00 – 2.99 21
3.00 – 3.99 4
4.00 – 4.99 2
5.00 – 5.99 1

9. Ogive
A line graph that depicts cumulative frequencies

10. Weights (pounds) of discard plastic
Example 3: Use the weights of discarded plastic in the frequency distribution below to construct an ogive. For the horizontal axis, use these class boundaries: –0.005, 0.995, 1.995, 2.995, 3.995, ,
Weights (pounds) of discard plastic
Frequency
0.00 – 0.99 14
1.00 – 1.99 20
2.00 – 2.99 21
3.00 – 3.99 4
4.00 – 4.99 2
5.00 – 5.99 1

12. Dot Plot
Consists of a graph in which each data value is plotted as a point (or dot) along a scale of values. Dots representing equal values are stacked.

13. Example 4: The following data represent scores of 34 students on a calculus test. Construct a dotplot. What does the dotplot suggest about the distribution of weights?

14. Stemplot (or Stem-and-Leaf Plot)
Represents quantitative data by separating each value into two parts: the stem (such as the leftmost digit) and the leaf (such as the rightmost digit)
Pulse Rates of Females

15. Example 5: The following data represent scores of 34 students on a calculus test. Construct a stemplot. What does the stemplot suggest about the distribution of weights?

16. 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.

17. Example 6: . Births are not, as you might think, evenly distributed across the days of the week. Here are the average numbers of babies born on each day of the week in 2003:
Present these data in a well-labeled bar graph.  

18. Multiple Bar Graph
Median Income of Males and Females

19. Pie Chart
A graph depicting qualitative data as slices of a circle, size of slice is proportional to frequency count

20. Scatter Plot (or Scatter Diagram)
A plot of paired (x, y) data with a horizontal x-axis and a vertical y-axis. Used to determine whether there is a relationship between the two variables

21. Time-Series Graph
Data that have been collected at different points in time: time-series data

22. Important Principles Suggested by Edward Tufte
For small data sets of 20 values or fewer, use a table instead of a graph.
A graph of data should make the viewer focus on the true nature of the data, not on other elements, such as eye-catching but distracting design features.
Do not distort data, construct a graph to reveal the true nature of the data.
Almost all of the ink in a graph should be used for the data, not the other design elements.

23. Important Principles Suggested by Edward Tufte
Don’t use screening consisting of features such as slanted lines, dots, cross-hatching, because they create the uncomfortable illusion of movement.
Don’t use area or volumes for data that are actually one-dimensional in nature. (Don’t use drawings of dollar bills to represent budget amounts for different years.)
Never publish pie charts, because they waste ink on nondata components, and they lack appropriate scale.