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Describing Data Graphically
Dr. Rick Jerz
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Goals
• Organize qualitative data into a frequency table and present this as a bar chart or a pie chart.
• Organize quantitative data into a frequency distribution.
• Present quantitative data as histograms, frequency polygons, and cumulative frequency polygons.
• Other chart types: Combination chart, such as a Pareto chart
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Chart Types
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Data Type & Chart Type
• Nominal• Bar chart and pie chart
• Ordinal Data• Bar chart
• Interval• Bar chart, histogram, frequency
polygon (line), cumulative frequency (ogive)
• Ratio• Bar chart, histogram, frequency
polygon (line), cumulative frequency (ogive)
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Levels of Measurement and Types of Variables
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Step 1: Data Collection
• What soda pop was preferred by children?
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Step 2: Data Organization
• A frequency distribution is a grouping of data into mutually exclusive categories showing the number of observations in each category
• Good for qualitative, and quantitativeinformation
• Frequency table
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Step 3: Create a Bar Chart
• A graph with categories on the horizontal axis and frequency on the vertical axis.
• Category frequencies are proportional to the heights of the bars
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Pie Charts (Nominal Data)
• A chart that shows the proportion, or percent, that each category represents of the total number of frequencies
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Relative Category Frequencies
• Category frequencies can be converted to relative category frequencies to show the fraction of the total number of observations in each category.
• A relative frequency captures the relationship between a category total and the total number of observations.
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Pie and Bar Charts
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Bar & Pie Charts: nOir Data
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Interval and Ratio Data Example
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Interval and Ratio Data: Categories are continuous!
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Interval Data Example:Prices of Vehicles Sold
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Constructing Frequency Tables for Interval & Ratio Data
Step 1: Decide on the number of categories. A useful rule to determine the number of categories (k) is the “2 to the k rule” such that 2k > n, where n is the number of data.
Step 2: Determine the category interval, or width.
The formula is: i ≥ (H-L)/k where i is the category interval, H is the highest observed value, L is the lowest observed value, and k is the number of categories. Use best judgment.
Step 3: Set the individual category limitsStep 4: Construct a frequency table16
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Example
• Step 1: There were 80 vehicles sold. So, n = 80. If we try k = 6, 26 = 64, 27 = 128, which means we would use 7 categories since 128 > 80
• Step 2: Calculate category width using (H-L)/k• ($35,925 - $15,546)/7 = $2,911 per category• Round up to some convenient number, such as a
multiple of 10 or 100. Use a category width of $3,000
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Resulting Categories
• Step 3: Set the individual category limits
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Step 4: Constructing a Frequency Table
• Step 4: Tally the vehicle selling prices into the categories. Count the number of items in each category.
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Relative Frequency Distribution
• Construct a relative frequency distribution by dividing each category frequency by the total number of observations.
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Histogram
Histogram is preferred!
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Frequency Polygon
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Cumulative Frequency Polygon
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Combination Chart
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Pareto Chart (Quality Control)
• Shows some form of quality problems, sorted from high to low, and the cumulative total is shown with a line
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Some Rules for Charting
• Keep charts simple• Avoid fancy 3D charts• Consider reproduction: avoid color• Scales can affect visual interpretation
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The Power of Relative Frequency Charts
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Microsoft Excel: Constructing Charts for Data
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