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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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