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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.
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 2.19 1.81 0.85 3.05 3.42 2.10
2.93 2.44 2.17 1.41 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 0.92 1.40 1.45 1.68 1.53
1.44 1.44 1.36 0.38 1.74 2.35 2.30 1.14 2.88 2.13
5.28 1.48 3.36 2.83 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
Relative Frequency PolygonUses relative frequencies (proportions or percentages) for the vertical scale.
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, 5.00 – 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
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, 4.995, 5.995.
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
Dot PlotConsists 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.
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?
72 59 73 72 74 74 61 67 6772 78 80 57 56 76 72 54 6588 74 57 83 68 79 73 71 70 65 67 76 67 72 76 53
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
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?
72 59 73 72 74 74 61 67 6772 78 80 57 56 76 72 54 6588 74 57 83 68 79 73 71 70 65 67 76 67 72 76 53
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.
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.
Pie ChartA graph depicting qualitative data as slices of a circle, size of slice is proportional to frequency count
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
Important PrinciplesSuggested 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.
Important PrinciplesSuggested 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.