Unit 2Section 2-3

2-3: Histograms, Frequency Polygons, and Ogives

Graphs are used to present data after it has been organized into frequency distributions.

The purpose of a graphs in statistics is to display data in pictorial form.

The three most commonly used graphs are: Histograms Frequency Polygons Ogives (pronounced: o-jive)

The Histogram

Histogram – a graph that displays data using contiguous vertical bars of various heights to represent the frequencies of the classes.

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How to Construct a Histogram Draw and label the x and y axis

Remember x is the horizontal axis and y is the vertical.

Represent the frequency on the y axis and the class boundaries on the x axis.

Using the frequency as the heights, draw vertical bars for each class.

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Activity: Construct a Histogram Using the data on the following

slide, construct a histogram to represent the data.

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Class Limit

Class Boundary

Tally Frequency

Cumulative

Frequency

100-104 99.5-104.5 || 2 2

105-109 104.5-109.5

|||||||| 8 10

110-114 109.5-114.5

||||||||||||||||||

18 28

115-119 114.5-119.5

||||||||||||| 13 41

120-124 119.5-124.5

||||||| 7 48

125-129 124.5-129.5

| 1 49

130-134 129.5-134.5

1 1 50

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The Frequency Polygon

Frequency Polygon – a graph that displays data by using lines that connect points plotted for the frequencies at the midpoints of the classes.

The frequencies are represented by the heights of the points.

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How to Construct a Frequency Polygon Find the midpoints of each class.

Add the upper and lower boundary, then divide by 2.

Draw and label the x and y axis Label the x-axis with the midpoint of each class. Determine a suitable scale for the frequencies.

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. The line should connect at the same distance where the

previous and next midpoint would be located.

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Activity: Construct a Frequency Polygon Using the data representing record

high data for the 50 states, construct a frequency polygon to represent the data.

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The Ogive

Ogive– a graph that represents the cumulative frequencies for the classes in a frequency distribution.

Also known as a cumulative frequency graph.

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How to Construct an Ogive Find the cumulative frequency of each class.

Draw and label the x and y axis Label the x-axis with the class boundaries of each

class. Determine a suitable scale for the frequencies.

Plot the cumulative frequency at each upper class boundary.

Starting with the first upper class boundary, connect adjacent points. Then extend the graph to the first lower class boundary on the x axis.

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Activity: Construct an Ogive Using the data representing record

high data for the 50 states, construct an Ogive to represent the data.

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Relative Frequency Graph

Relative Frequency Graph– a graph that coverts the distributions from frequencies to proportions of frequencies.

To covert, divide the frequency by the overall cumulative frequency.

The sum of the relative frequencies will always equal 1.

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