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b a c kn e x t h o m e Frequency Distributions frequency distribution A frequency distribution is a table used to organize data. The left column (called classes or groups) includes numerical intervals on a variable being studied. The right column is a list of the frequencies, or number of observations, for each class. Intervals are normally of equal size, must cover the range of the sample observations, and be non-overlapping.

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b a c kn e x t h o m e Construction of a Frequency Distribution n Rule 1: Intervals (classes) must be inclusive and non-overlapping; n Rule 2: Determine k, the number of classes; n Rule 3: Intervals should be the same width, w; the width is determined by the following: Both k and w should be rounded upward, possibly to the next largest integer.

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b a c kn e x t h o m e Construction of a Frequency Distribution Quick Guide to Number of Classes for a Frequency Distribution Sample SizeNumber of Classes Fewer than 505 – 6 classes 50 to 1006 – 8 classes over 1008 – 10 classes

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b a c kn e x t h o m e Cumulative Frequency Distributions cumulative frequency distribution A cumulative frequency distribution contains the number of observations whose values are less than the upper limit of each interval. It is constructed by adding the frequencies of all frequency distribution intervals up to and including the present interval.

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b a c kn e x t h o m e Relative Cumulative Frequency Distributions relative cumulative frequency distribution A relative cumulative frequency distribution converts all cumulative frequencies to cumulative percentages

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b a c kn e x t h o m e Histograms and Ogives histogram A histogram is a bar graph that consists of vertical bars constructed on a horizontal line that is marked off with intervals for the variable being displayed. The intervals correspond to those in a frequency distribution table. The height of each bar is proportional to the number of observations in that interval.

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b a c kn e x t h o m e Histograms and Ogives ogive, An ogive, sometimes called a cumulative line graph, is a line that connects points that are the cumulative percentage of observations below the upper limit of each class in a cumulative frequency distribution.

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b a c kn e x t h o m e Histogram and Ogive for Example 2.1

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b a c kn e x t h o m e Stem-and-Leaf Display stem-and-leaf display A stem-and-leaf display is an exploratory data analysis graph that is an alternative to the histogram. Data are grouped according to their leading digits (called the stem) while listing the final digits (called leaves) separately for each member of a class. The leaves are displayed individually in ascending order after each of the stems.

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b a c kn e x t h o m e Stem-and-Leaf Display Stem-and-Leaf Display for Gilotti’s Deli Example

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b a c kn e x t h o m e Tables - Bar and Pie Charts - Frequency and Relative Frequency Distribution for Top Company Employers Example

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b a c kn e x t h o m e Tables - Bar and Pie Charts - Figure 2.9 Bar Chart for Top Company Employers Example

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b a c kn e x t h o m e Tables - Bar and Pie Charts - Figure 2.10 Pie Chart for Top Company Employers Example

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b a c kn e x t h o m e Pareto Diagrams Pareto diagram Pareto diagramvital few trivial many. A Pareto diagram is a bar chart that displays the frequency of defect causes. The bar at the left indicates the most frequent cause and bars to the right indicate causes in decreasing frequency. A Pareto diagram is use to separate the “vital few” from the “trivial many.”

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b a c kn e x t h o m e Line Charts line chart, time plot, A line chart, also called a time plot, is a series of data plotted at various time intervals. Measuring time along the horizontal axis and the numerical quantity of interest along the vertical axis yields a point on the graph for each observation. Joining points adjacent in time by straight lines produces a time plot.

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b a c kn e x t h o m e Line Charts

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