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Frequency Distributions and Graphs.  Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives.

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Presentation on theme: "Frequency Distributions and Graphs.  Represent data in frequency distributions graphically using histograms, frequency polygons, and ogives."— Presentation transcript:

1 Frequency Distributions and Graphs

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

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

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

5  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

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

7 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.

8  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.

9 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

10 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.

11  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.

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

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

14 Pareto Chart for the number of Crimes Investigated by Law

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

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

17  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.

18 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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