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Lesson 143:  Working with Histograms

In this very easy lesson we'll look at how to create a histogram from a frequency or cumulative frequency table. 

Before starting this lesson, be sure that you fully understand the previous lesson.  In this lesson, we'll be using the data in the previous lesson to make special graphs called histograms.  A histogram is just a bar chart that represents the data in a frequency table.  You've worked with bar charts even in the very early lessons.  A histogram always has vertical bars, and there is never any space between them.  I used Microsoft Excel to make these charts, but you can easily use graph paper, which is what you'll use on a test. 

The first chart is based on the interval frequency table in the previous lesson.  Notice how I labeled my graph at the top.  I also labeled each of the axes.  You can see that each horizontal line represents one unit of frequency.  Depending on your data, you might need to make each line equal to a larger number, like two or five.  Each bar is labeled so that is easy to see what interval it represents.  I happened to use blue for my bars, but if you were using pencil, you would just lightly shade in each bar, and make sure that you have a dark line in between each bar so that you can see where each new bar begins.

Frequency Histogram

In this next histogram, I've made a chart of the scores from the cumulative frequency histogram in the previous lesson.  I did all the same things that I did for the histogram above, such as labeling the axes.  Notice how I chose to make each horizontal line represent a frequency of 2.  The minor (short) tick marks show that in between each line is a unit of 1.  Always decide on what will be the best scale for your axes.  If we had very large frequencies, we might choose for each bar line to represent five, ten, or even more.

Cumulative Frequency Histogram

When making a histogram by hand on graph paper, you will often omit the horizontal bar lines that do not represent the frequency of any interval.  In other words, you will only put in horizontal bar lines that connect to the top of each of your vertical interval bars.  This way, it is easy to look at the top of an interval bar, and then trace the horizontal line over to the left, to see what frequency or cumulative frequency the bar represents. 

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