1. Section 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

2. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Should be able to stand alone without the original data. Must have a title and labels for both axes. When appropriate, a legend, a source, and a date should be included. Graphs:

3. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Shows how large each category is in relation to the whole. Pie Chart: Create a pie chart from the following information: Types of Housing Number of Students Apartment20 Dorm15 House9 Sorority/Fraternity House5

4. Solution: Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists 100%100˚ AnglesFrequency

5. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Create a bar graph from the following information: Types of Housing Number of Students Apartment20 Dorm15 House9 Sorority/Fraternity House5 Notice that the bar graph shown is in descending order of largest to smallest. This type of bar graph is called a Pareto chart and is typically used with nominal data.

6. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Create a side-by-side bar graph from the following information: Types of Housing Number of Students from Class A Number of Students from Class B Apartment2013 Dorm1524 House96 Sorority/Fraternity House 57

7. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Create a stacked bar graph from the following information: Types of Housing Number of Students from Class A Number of Students from Class B Apartment2013 Dorm1524 House96 Sorority/Fraternity House 57 With the stacked bar graph, it is easier to see that more students live in the dorms than in apartments.

8. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists A bar graph of a frequency distribution. The horizontal axis is a real number line. The width of the bars represent the class width from the frequency table and should be uniform. The bars should touch. The height of each bar represents the frequency of the class it represents. Histograms:

9. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Create a histogram from the following information: Plasma Screen TV Prices ClassfMidpointBoundaries $1500 – $159921549.51499.5 – 1599.5 $1600 – $169951649.51599.5 – 1699.5 $1700 – $179941749.51699.5 – 1799.5 $1800 – $189951849.51799.5 – 1899.5 $1900 – $199941949.51899.5 – 1999.5 Although we use the class boundaries to draw the histograms, it is appropriate to use either the class boundaries (shown in the figure to the left) or midpoints (shown in the figure to the right) when labeling the x-axis.

10. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists A visual display of the frequencies of each class using the midpoints from a frequency table. Frequency Polygons: 1.Mark the class boundaries on the x-axis and the frequencies on the y-axis. Note that extra classes at the lower and upper ends will be added, each having a frequency of 0. From the previous example of plasma TV prices, these classes will be 1400 – 1499 at the lower end and 2000 – 2099 at the upper end. Steps for creating a frequency polygon:

11. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists 2.Add the midpoints to the x-axis and plot a point at the frequency of each class directly above its midpoint. Notice that the class boundaries have been lightened. This is due to the fact that a frequency polygon represents the midpoints of the data. Steps for creating a frequency polygon (continued): 3.Join each point to the next with a line segment.

12. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists A line graph which depicts the cumulative frequency of each class from a frequency table. Ogives: 1.Begin by tabulating the cumulative frequencies for each class. Steps for creating an ogive: Plasma Screen TV Prices Classf Cumulative Frequencies Boundaries $1500 – $1599221499.5 – 1599.5 $1600 – $1699571599.5 – 1699.5 $1700 – $17994111699.5 – 1799.5 $1800 – $18995161799.5 – 1899.5 $1900 – $19994201899.5 – 1999.5

13. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists 2.Unlike a frequency polygon where two classes are added, we only include an extra class at the lower end for this graph, giving it a frequency of 0. 3.Next, plot a point at the cumulative frequency for each class directly above its upper class boundary. Steps for creating an ogive (continued): 4.Finally, join the points together with line segments.

14. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Retain the original data. The leaves are usually the last digit in each data value and the stems are the remaining digits. Stem and Leaf Plots: 1.Create two columns, one on the left for stems and one on the right for leaves. 2.List each of the stems that occur in the data set in numerical order. 3.List each leaf next to its stem. 4.Create a key to guide interpretation of the stem and leaf plot. 5.The leaves may then be put in order, if desired, to create an ordered stem and leaf plot. Steps for creating a stem and leaf plot:

15. Graphical Descriptions of Data 2.2 Graphical Displays of Data HAWKES LEARNING SYSTEMS math courseware specialists Create a steam and leaf plot from the following information: ACT Scores 1823243119 2726223218 3527292420 1817212526 Key: 1|8 = 18 ACT Scores LeavesStem 1 2 3 8 3 1 9 4 2 8 7 5 8 6 7 27940165 Key: 1|8 = 18 Ordered Array ACT Scores LeavesStem 1 2 3 7 0 1 8 1 2 8 2 5 8 3 9 44566797