Course A in Business Statistics
4th Edition
Chapter 2 Graphs, Charts, and Tables Describing Your Data
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 21
Chapter Goals
After completing this chapter, you should be able to:
Construct a frequency distribution both manually and with a computer Construct and interpret a histogram Create and interpret bar charts, pie charts, and stem-and-leaf diagrams Present and interpret data in line charts and scatter diagrams
Chap 22
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Frequency Distributions
What is a Frequency Distribution?
A frequency distribution is a list or a table ... containing the values of a variable (or a set of ranges within which the data falls) ... and the corresponding frequencies with which each value occurs (or frequencies with which data falls within each range)
Chap 23
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Why Use Frequency Distributions?
A frequency distribution is a way to summarize data The distribution condenses the raw data into a more useful form... and allows for a quick visual interpretation of the data
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 24
Frequency Distribution: Discrete Data
Discrete data: possible values are countable
Example: An advertiser asks 200 customers how many days per week they read the daily newspaper.
Number of days read
0 1 2 3 4 5 6 7 Total
Frequency
44 24 18 16 20 22 26 30 200
Chap 25
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Relative Frequency
Relative Frequency: What proportion is in each category?
Number of days read
0 1 2 3 4 5 6 7 Total
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Frequency
44 24 18 16 20 22 26 30 200
Relative Frequency
.22 .12 .09 .08 .10 .11 .13 .15 1.00
44 = .22 200
22% of the people in the sample report that they read the newspaper 0 days per week
Chap 26
Frequency Distribution: Continuous Data
Continuous Data: may take on any value in some interval
Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature 24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27
(Temperature is a continuous variable because it could be measured to any degree of precision desired)
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc. Chap 27
Grouping Data by Classes
Sort raw data in ascending order:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Find range: 58 - 12 = 46 Select number of classes: 5 (usually between 5 and 20) Compute class width: 10 (46/5 then round off) Determine class boundaries:10, 20, 30, 40, 50 Compute class midpoints: 15, 25, 35, 45, 55 Count observations & assign to classes
Chap 28
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Frequency Distribution Example
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 Frequency Distribution
Class 10 but under 20 20 but under 30 30 but under 40 40 but under 50 50 but under 60 Total
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Frequency
Relative Frequency
3 6 5 4 2 20
.15 .30 .25 .20 .10 1.00
Chap 29
Histograms
The classes or intervals are shown on the horizontal axis frequency is measured on the vertical axis Bars of the appropriate heights can be used to represent the number of observations within each class Such a graph is called a histogram
Chap 210
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Histogram Example
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Histogram 7 6 Frequency 5 4 3 2 1 0 0 5 15 25 36 45 55 3 2 0 More
Chap 211
6 5 4
No gaps between bars, since continuous data
Class Midpoints
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Questions for Grouping Data into Classes
1. How wide should each interval be?
(How many classes should be used?)
2. How should the endpoints of the intervals be determined?
Often answered by trial and error, subject to user judgment The goal is to create a distribution that is neither too "jagged" nor too "blocky" Goal is to appropriately show the pattern of variation in the data
Chap 212
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
How Many Class Intervals?
Many (Narrow class intervals)
3.5 3 Frequency 2.5 2 1.5 1 0.5 0 More 12 16 20 24 28 32 36 40 44 48 52 56 60 4 8
may yield a very jagged distribution with gaps from empty classes Can give a poor indication of how frequency varies across classes
Temperature
12 10 Frequency
Few (Wide class intervals)
8 6 4 2 0 0 30 60 More Temperature
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
may compress variation too much and yield a blocky distribution can obscure important patterns of variation.
(X axis labels are upper class endpoints) Chap 213
General Guidelines
Number of Data Points
Number of Classes
under 50 50 100 100 250 over 250
5- 7 6 - 10 7 - 12 10 - 20
Class widths can typically be reduced as the number of observations increases Distributions with numerous observations are more likely to be smooth and have gaps filled since data are plentiful
Chap 214
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Class Width
The class width is the distance between the lowest possible value and the highest possible value for a frequency class The minimum class width is
W = Largest Value - Smallest Value Number of Classes
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 215
Histograms Excel
1 in Select Tools/Data Analysis
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 216
Histograms in Excel
(continued)
2 Choose Histogram
3 Input data and bin ranges
Select Chart Output
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc. Chap 217
Stem and Leaf Diagram
A simple way to see distribution details in a data set METHOD: Separate the sorted data series into leading digits (the stem) and the trailing digits (the leaves)
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 218
Example:
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Here, use the 10's digit for the stem unit:
Stem Leaf
12 is shown as 35 is shown as
1
2
3
5
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 219
Example:
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Completed Stem-and-leaf diagram:
Stem Leaves
1 2 3 4 5
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
2 3 7 1 4 4 6 7 8 0 2 5 7 8 1 3 4 6 3 8
Chap 220
Using other stem units
Using the 100's digit as the stem:
Round off the 10's digit to form the leaves
Stem
Leaf
613 would become 776 would become ... 1224 becomes
6 7 12
1 8 2
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 221
Graphing Categorical Data
Categorical Data
Pie Charts
Bar Charts
Pareto Diagram
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 222
Bar and Pie Charts
Bar charts and Pie charts are often used for qualitative (category) data Height of bar or size of pie slice shows the frequency or percentage for each category
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 223
Pie Chart Example
Current Investment Portfolio
Investment Type
(in thousands $)
Amount
Percentage
Stocks Bonds CD Savings Total
46.5 32.0 15.5 16.0 110
42.27 29.09 14.09 14.55 100
Savings 15% CD 14%
Stocks 42%
(Variables are Qualitative)
Bonds 29%
Percentages are rounded to the nearest percent
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 224
Bar Chart Example
Investor's Portfolio
Savings CD Bonds Stocks 0 10 20 30 40 50
Amount in $1000's
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc. Chap 225
Pareto Diagram Example
45% 100% 90%
% invested in each category (bar graph)
40%
35%
80%
cumulative % invested (line graph)
70% 30% 60% 25% 50% 20% 40% 15% 30% 10% 20%
5%
10%
0% Stocks Bonds Savings CD
0%
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 226
Bar Chart Example
Number of days read Frequency
Newspaper readership per week
50 40 Freuency 30 20 10 0 0 1 2 3 4 5 6 7 Number of days newspaper is read per week
0 1 2 3 4 5 6 7 Total
44 24 18 16 20 22 26 30 200
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Chap 227
Tabulating and Graphing Multivariate Categorical Data
Investment in thousands of dollars
Investor A Investor B Investor C Total
Investment Category
Stocks Bonds CD Savings Total
46.5 32.0 15.5 16.0 110.0
55 44 20 28 147
27.5 19.0 13.5 7.0 67.0
129 95 49 51 324
Chap 228
A Course In Business Statistics, 4th 2006 PrenticeHall, Inc.
Tabulating and Graphing Multivariate Categorical Data
(continued)
Side by side charts
Comparing Investors
S avings CD B onds S toc k s 0 10 Inves tor A 20 30 ...