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