Statistics for Modern Business Decisions

1
Statistics for Modern Business Decisions

• Professor Monnie McGee
• Department of Statistical Science
• Lecture 2 Displaying Data

2
Lecture 2 Highlights

• Topics (PBS Section 1.1)
• Numerical Categorical Data (Review pages 4 5)
• Bar Charts and Pie Charts (pp. 7 9)
• Histograms (pp. 10 18)
• Assignments
• Due ASAP
• Print Out, Read, and Sign the Course Information
  Documentfrom course web site (Mandatory
  Assignment)
• Try to log in to WebCT before Fridays lab.
• Homework 1 due Friday, September 5, at beginning
  of lab
• 1.14, 1.18 (part c on following page), 1.28
• Problems begin on page 24

3
Charts 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 dont 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

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5
Distribution of Accidents Involving Firestone
Tires in 2000
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Pareto Chart of Firestone Data
8
Apply 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.

9
Graphs for Quantitative Variables

• 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

10
Frequency Distributionsfor 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)

Always Round Up!!
Largest - Smallest
Width of Interval
Just Round
Number of Classes
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Examining a Distribution (p. 14)

• 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

15
Creating 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?

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Average Salaries for 30 Major League Baseball
Teams on Opening Day of the 2000 Season
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Distribution of Individual Salaries of Cincinnati
Reds Players on Opening Day of the 2000 Season
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Distribution of Monthly Returns for all U.S.
Common Stocks from 1951 - 2000
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Variables 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

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Annual Orange Price Index, 1991 - 2001
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Index 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

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Seasonally Adjusted Monthly Unemployment Rate
January 1990-August 2001