section 2.2 graphical displays of data hawkes learning systems math courseware specialists copyright...

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.

Graphical Descriptions of Data

2.2 Graphical Displays of Data



• 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:





Shows how large each category is in relation to the whole.

Pie Chart:

Create a pie chart from the following information:

Types of Housing

Types of Housing Number of Students

Apartment 20

Dorm 15

House 9

Sorority/Fraternity House 5

Solution:





100% 100˚

AnglesFrequency





Create a bar graph from the following information:

Types of Housing

Types of Housing Number of Students

Apartment 20

Dorm 15

House 9

Sorority/Fraternity House 5

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.





Create a side-by-side bar graph from the following information:

Types of Housing

Types of Housing

Number of Students

from Class A

Number of Students

from Class B

Apartment 20 13

Dorm 15 24

House 9 6

Sorority/Fraternity House

5 7





Create a stacked bar graph from the following information:

Types of Housing

Types of Housing

Number of Students

from Class A

Number of Students

from Class B

Apartment 20 13

Dorm 15 24

House 9 6

Sorority/Fraternity House

5 7

With the stacked bar graph, it is easier to see that more students live in the dorms than in apartments.





• 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:





Create a histogram from the following information:

Plasma Screen TV Prices

Class f Midpoint Boundaries

$1500 – $1599 2 1549.5 1499.5 – 1599.5

$1600 – $1699 5 1649.5 1599.5 – 1699.5

$1700 – $1799 4 1749.5 1699.5 – 1799.5

$1800 – $1899 5 1849.5 1799.5 – 1899.5

$1900 – $1999 4 1949.5 1899.5 – 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.





• 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:





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.





• 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

Class fCumulative Frequencies

Boundaries

$1500 – $1599 2 2 1499.5 – 1599.5

$1600 – $1699 5 7 1599.5 – 1699.5

$1700 – $1799 4 11 1699.5 – 1799.5

$1800 – $1899 5 16 1799.5 – 1899.5

$1900 – $1999 4 20 1899.5 – 1999.5





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.





• 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:





Create a steam and leaf plot from the following information:

ACT Scores

18 23 24 31 19

27 26 22 32 18

35 27 29 24 20

18 17 21 25 26

Key: 1|8 = 18

ACT ScoresLeavesStem

123

831

942

875

86

72 7 9 4 0 1 65

Key: 1|8 = 18Ordered Array

ACT ScoresLeavesStem

123

701

812

825

83

94 4 5 6 6 7 97

section 2.2 graphical displays of data hawkes learning systems math courseware specialists copyright...

Documents

graphical descriptions

original data

nominal data

stacked bar graph

anglesfrequency slide

type of bar graph

following information

class width