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Frequency Distributions and Graphs

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Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives.

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The three most commonly used graphs in research are: The histogram. The frequency polygon. The cumulative frequency graph, or ogive (pronounced o-jive).

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histogram The histogram is a graph that displays the data by using vertical bars of various heights to represent the frequencies.

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Draw and label the x and y axes frequency class boundaries Represent the frequency on the y axis and the class boundaries on the x axis Using the frequencies as heights, draw vertical bars for each class

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For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a histogram. Class LimitsFrequency 90 – – – – – 1349

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frequency polygon A frequency polygon is a graph that displays the data by using lines that connect points plotted for frequencies at the midpoint of classes. The frequencies represent the heights of the midpoints.

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Find the midpoints for each class frequency midpoints Draw the x and y axes. Label the frequency on the y axis and the midpoints on the x axis. Using the midpoints for the x values and the frequencies as the y values, plot the points. Connect the adjacent points with line segments. Draw a line back to the x axis at the beginning and end of the graph.

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Frequency Polygon For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a frequency polygon. Class LimitsFrequency 90 – – – – – Number of college applicants F r e q u e n c y

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cumulative frequency graph ogive A cumulative frequency graph or ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

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Find the cumulative frequency for each class cumulative frequenciesclass boundaries Draw the x and y axes. Label the cumulative frequencies on the y axis and the class boundaries on the x axis. Plot the cumulative frequency at each upper boundary. Starting with the first upper boundary; connect the adjacent points with straight lines. Then extend the graph to the first lower class boundary on the x axis.

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For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct an ogive. Class LimitsFrequency 90 – – – – – 1349

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Pareto charts - Pareto charts - a Pareto chart is used to represent a frequency distribution for a categorical variable.

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Pareto Chart for the number of Crimes Investigated by Law

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Time series graph - Time series graph - A time series graph represents data that occur over a specific period of time.

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Year R i d e r s h i p ( i n m i l l i o n s ) PORT AUTHORITY TRANSIT RIDERSHIP

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Pie graph - Pie graph - A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

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Robbery (29, 12.1%) Rape (34, 14.2%) Assaults (164, 68.3%) Homicide (13, 5.4%) Pie Chart of the Number of Crimes Investigated by Law Enforcement Officers In U.S. National Parks During 1995

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