Statistics and Business Decisions

1. 1
Statistics for Modern BusinessStatistics for Modern Business
DecisionsDecisions
Topic 2: Displaying Data

2. 2
Charts for Categorical VariablesCharts for Categorical Variables
• Bar Charts
– Each bar represents a category
– Height of bar corresponds to percentage or frequency of data in
that category
– Can display 2 variables simultaneously (called a clustered bar
chart)
– Percents don’t have to sum to 100
– Best for comparing categories
– Pareto charts are bar charts where the bars are arranged in
descending order of frequency from left to right.
• Pie Charts
– Each slice of the pie represents a category
– Size of slices correspond to percentage
– Must sum to 100%
– Best for showing percentage of the whole

3. 3
Political Leanings of Stat 2301 Fall 2003 Class
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Cons Lib Mod
DropPageFields Here
Count of Politics
Politics
Drop More Series Fields Here

4. 4
Distribution of Accidents Involving Firestone Tires in 2000

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6. 6
Pareto Chart of Firestone Data

7. 7
Apply Your KnowledgeApply Your Knowledge
In 1999 there were 6023 job-related deaths in the United States.
Among these were 807 deaths in agriculture-related jobs, 121 in
mining, 1190 in construction, 719 in manufacturing, 1006 in
transportation and public utilities, 237 in wholesale trade, 507 in
retail trade, 105 in finance-related jobs, 732 in service-related
jobs, and 562 in government jobs.
• Find the percent of occupational deaths for each of these job
categories, rounded to the nearest whole percent. What percent
of job-related deaths were in categories not listed here?
• Make a well-labeled bar graph of the distribution of
occupational deaths. Be sure to include the “other occupations”
bar.
• Make a well-labeled Pareto chart of these data. What percent of
all occupational deaths are accounted for by the first three
categories in your Pareto chart?
• Would it also be correct to use a pie chart to display these data?
Explain.

8. 8
Graphs for QuantitativeGraphs for Quantitative
VariablesVariables
• Quantitative variables often take many values
• Makes more sense to group nearby values into
intervals
• Histogram
– Displays shape, variability and outliers
– The height of each bar represents the count or percent of
values in an interval.
– Bars must cover the entire range of values of a variable
– No space between bars unless an interval is empty
– No right way to choose number of intervals – use best
judgment to display shape of the data

9. 9
Frequency DistributionsFrequency Distributions
for Numerical Datafor Numerical Data
Class Intervals
– Select the Number of Classes (approx. 5-15)
– Use a Common Width for Each Class (when possible)
– Make Classes Mutually Exclusive & Exhaustive
(Each Data Value Can be Placed in One
and Only One Class)
Width of Interval =
Largest - Smallest
Number of Classes
# n=
Just Round
Always Round Up!!

10. 10
Student Heights
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60 63 66 69 72 75 78
Right Endpoint of Height
Frequency

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13. 13
Examining a DistributionExamining a Distribution
• Look for the overall pattern
• Look for striking deviations from that pattern
• Overall pattern of histogram is described by its
shape, center, and spread
– Shape: symmetric, right-skewed and left-skewed
– Center: value which divides the data values approximately
in half (or where the histogram will balance)
– Spread: largest in smallest values
• Outliers are individual values that deviate from
the overall pattern

14. 14
Creating a HistogramCreating a Histogram
• EPA regulations require automakers to give the
city and highway gas mileages for each model of
car. Table 1.2 gives the highway mileages for 32
midsize 2001 model year cars.
• Make a histogram of the highway mileages of
these cars
• Describe the main features of the distribution of
highway mileage
• The government imposes a “gas guzzler” tax on
cars with low gas mileage. Do you think that any
of these cars are subject to the tax?

15. 15

16. 16
Average Salaries for 30 Major League
Baseball Teams on Opening Day of the 2000 Season

17. 17
Distribution of Individual Salaries of Cincinnati Reds
Players on Opening Day of the 2000 Season

18. 18
Distribution of Monthly Returns for all
U.S. Common Stocks from 1951 - 2000

19. 19
Variables Measured Over TimeVariables Measured Over Time
• Cross-sectional data: information concerning a
group of individuals at one time
• Time Series: measurements of a variable taken at
regular intervals over time
• Time plot: Plot observation against the time at
which it was measured
– Time is on horizontal axis, variable on vertical
– Connect data points to emphasize changes over time
• Overall Patterns
– Seasonal variation: a pattern that repeats itself at known
regular intervals of time
– Trend: persistent, long-term rise or fall
– Cycles: Irregular but clear up and down movements

20. 20
Annual Orange Price Index, 1991 - 2001

21. 21
Index NumbersIndex Numbers
• Note on vertical axis of previous slide “1982 –
84 = 100)
• Index number gives current value as a
percentage of a base value (CPI)
• Based on survey of prices of goods and services
collected by the government
• Nationwide average price that is less variable
than prices at individual stores

22. 22
Seasonally Adjusted Monthly Unemployment Rate
January 1990-August 2001

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• SOURCE: www.smu.edu/statistics/resources/2301.html--business