Graphical Displays of Data

Section 2.2

Objectives

• Create and interpret the basic types of graphs used to display data

Introduction

• A graph is a snapshot that allows us to view patterns at a glance without undergoing lengthy analysis of the data.

• Graphs are much more visually appealing than a table or list.

• A graph should be able to stand alone, without the original data. Graph must be given a title, as well as labels for both axes.

Purpose of Statistical Graphs

• To convey the data to the viewers in pictorial form– It is easier for most people to comprehend the meaning of

data presented as a picture than data presented as a table. This is especially true if the viewers have little or no statistical knowledge

• To describe the data set• To analyze the data set (Distribution of data set)• To summarize a data set• To discover a trend or pattern in a situation over a

period of time• To get the viewers’ attention in a publication or

speaking presentation

Graphs Used to Display Qualitative Data

Pie Chart• Pie Chart is a circle that

is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

• Show relationship of the parts to the whole

Pareto Chart*

• Bar graph• Used to represent a

frequency distribution for a categorical variable (nominal level) and the frequencies are displayed by the heights of the contiguous vertical bars, which are arranged in order from highest to lowest.

How do I create a Pareto Chart from a categorical frequency distribution?

• STEP 1: Draw the x- and y-axes• STEP 2: Label the x-axis using the qualitative

categories (highest frequency to lowest frequency)

• STEP 3: Label the y-axis using an appropriate scale that encompasses the high and low frequencies

• STEP 4: Draw the contiguous vertical bars

Example Nursing Business Admin Education

Computer Info Systems Political Science Art

General Studies Nursing Education

Education Psychology Business Admin

Psychology Business Admin General Studies

General Studies General Studies History

History History General Studies

Education Computer Info Systems Nursing

Education General Studies Education

History

Class (Major) Frequency Percentage

Art 1 3.6%

Business Administration

3 10.7%

Computer Info Systems

2 7.1%

Education 6 21.4%

General Studies 6 21.4%

History 4 14.3%

Nursing 3 10.7%

Political Science 1 3.6%

Psychology 2 7.1%

TOTAL 28 100%

Other Bar Graphs

Side-by-Side Bar Graph• Used to compare different

groups• Typically, uses different

colored bars to distinguish groups

Stacked Bar Graph

Histogram*

• A bar graph that displays the data from a frequency distribution– Horizontal Scale (x-axis)

is labeled using CLASS BOUNDARIES or MIDPOINTS

– Vertical Scale (y-axis) is labeled using frequency

– NOTE: bars are contiguous (No gaps)

How do I create a histogram from a grouped frequency distribution?

• MINITAB– Enter raw data into MINITAB

Ages of NASCAR Nextel Cup Drivers in Years (NASCAR.com) (Data is ranked---Collected Spring 2008)

21 21 21 23 23 23 24 25

25 26 26 26 26 27 27 28

28 28 28 29 29 29 29 30

30 30 30 31 31 31 31 31

32 34 35 35 35 36 36 37

37 38 38 39 41 42 42 42

43 43 43 44 44 44 44 45

45 46 47 48 48 48 49 49

49 50 50 51 51 65 72

Example-Construct a histogram of the ages of Nextel Cup Drivers. Use the class boundaries as the scale on the x-axis

Frequency Polygon

• Line graph (rather than a bar graph)

• Uses class midpoints rather than class boundaries on x-axis

Ogive (Cumulative Frequency Polygon)

• Line graph (rather than a bar graph)

• Uses class boundaries on x-axis

• Uses cumulative frequencies (total as you go) rather than individual class frequencies

• Used to visually represent how many values are below a specified upper class boundary

Another possibility

• We can use the percentage (relative frequency) rather than the “tallies” (frequency) on the x-axis. – Relative Frequency

Histogram– Relative Frequency

Polygon– Relative Frequency

Ogive

• Used when a comparison between two data sets is desired, especially if the data sets are two different sizes

• Overall shape (distribution) of graph is the same, but we use a % on the y-axis scale

Stem and Leaf Plot*

– Method for organizing data

– Combination of sorting and graphing

– Original Data is retained unlike with a grouped frequency distribution

– “Leaves” are usually the last digit in each data value; right hand column of two-column table

– “Stems” are remaining digits ; left hand column of two-column table

Dotplot*(not in text)

– Graph in which each data value is plotted as a point (or dot) along a single horizontal scale of values.

– Dots representing equal values are stacked

– Original data is retained

Exam #1 Scores in Mrs. Ralston’s Math 1111 classes in Fall 2008 39 40 41 43 50 59 59 61 63 64

65 66 66 68 70 70 70 71 73 73

75 76 77 78 79 79 80 80 80 80

81 81 82 83 84 84 84 84 85 86

86 87 88 89 89 90 90 90 90 91

91 92 94 94 94 94 95 96 96 98

99 100 100 100 100

• Construct a frequency distribution for the Exam #1 scores. Use 8 classes with a class width of 10 beginning with a lower class limit of 30.

• Use the raw data to construct a histogram of the Exam #1 scores in MINITAB

• Use the raw data to construct a dotplot of the Exam #1 scores in MINITAB

Homework

• Page 71 #2 and 3 (create a Pareto Chart)• Page 74 #16 (create a Stem and Leaf Plot)• Worksheet