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**Frequency Distributions and Graphs**

Chapter 2 Frequency Distributions and Graphs

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

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**2-3 Histograms, Frequency Polygons, and Ogives**

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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**2-3 Histograms, Frequency Polygons, and Ogives**

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

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**Procedure for Drawing a Histogram**

Draw and label the x and y axes 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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Example of a Histogram For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a histogram. Class Limits Frequency 90 – 98 6 99 – 107 22 108 – 116 43 117 – 125 28 126 – 134 9 134.5 1 25.5 16.5 07.5 98.5 89.5 60 50 40 30 20 10 Number of college applicants F r e q u n c y

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**2-3 Histograms, Frequency Polygons, and Ogives**

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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**Procedure for Drawing a Frequency Polygon**

Find the midpoints for each class 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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**Example of a Frequency Polygon**

For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct a frequency polygon. Frequency Polygon Class Limits Frequency 90 – 98 6 99 – 107 22 108 – 116 43 117 – 125 28 126 – 134 9 60 50 y c n 40 e u q 30 e r F 20 10 94 103 112 121 130 Number of college applicants

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**2-3 Histograms, Frequency Polygons, and Ogives**

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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**Procedure for Drawing a Cumulative Frequency Graph**

Find the cumulative frequency for each class 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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Example of an Ogive For 108 randomly selected college applicants, the following frequency distribution for entrance exam scores was obtained. Construct an ogive. Ogive 125.5 116.5 107.5 98.5 89.5 120 100 80 60 40 20 Number of college applicants Cumulative Frequency 134.5 Class Limits Frequency 90 – 98 6 99 – 107 22 108 – 116 43 117 – 125 28 126 – 134 9

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2-4 Other Types of Graphs Pareto charts - a Pareto chart is used to represent a frequency distribution for a categorical variable.

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**Example of a Pareto Chart**

i c d e R b r y a p Assault 1 3 2 9 4 6 5 . 8 P a r e t o C h a r t f o r t h e n u m b e r o f C r i m e s I n v e s t i g a t e d b y L a w D e f c t C o u n P r m % E ment Officers in U.S. National Parks During 1995.

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2-4 Other Types of Graphs Time series graph - A time series graph represents data that occur over a specific period of time.

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**2-4 Other Types of Graphs - Time Series Graph**

U T H O R I T Y T R A N S I T R I D E R S H I P 8 9 ) s 8 7 n o i i l l 8 5 m n 8 3 ( i p 8 1 i h s r 7 9 e d i R 7 7 7 5 1 9 9 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 Y e a r

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2-4 Other Types of Graphs 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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**2-4 Other Types of Graphs - Pie Graph**

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

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