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LESSON: Histograms

READ: Make a Frequency Table and a Histogram given Unorganized Data

Make a Frequency Table and a Histogram given Unorganized Data

Sometimes, you will be given a set of data that you will need to organize. This data will be unorganized. To work with it, you will have to organize it by creating a frequency table. Then you can use that frequency table to create a histogram.

Let’s look at an example.


Fifteen people were asked to state the number of hours they exercise in a seven day period. The results of the survey are listed below. Make a frequency table and histogram to display the data.

8, 2, 4, 7.5, 10, 11, 5, 6, 8, 12, 11, 9, 6.5, 10.5, 13

First arrange the data on a frequency table. Recall that a table with three columns needs to be drawn: one for intervals, one for tallied results, and another for frequency results. The range in values for this set of data is eleven. Therefore, data will be tallied in intervals of three.

Hours of Exercise Tally Frequency
0 – 2 I 1
3 – 5 I I 2
6 – 8 I I I I I 5
9 – 11 I I I I I 5
12 – 14 I I 2

Next, the data needs to be displayed on a histogram. Recall that a horizontal (x) and vertical (y) axis needs to be drawn. List the intervals across the horizontal axis. Name this axis “Hours of Exercise.” Label the vertical axis by ones. Title the vertical axis “Frequency.” For each set of intervals, draw vertical columns the appropriate frequency. Color in the vertical columns and ensure that no space is between them. Title the graph “Hours of Exercise.”

Now let’s make some conclusions based on the information displayed in the histogram.

Looking at the histogram above, you can that equal numbers of people reported that they exercise between six and eight and nine and eleven hours each week. Two people stated that they exercise between three and five hours per week. Two people reported that they exercise between twelve and fourteen hours per week. Zero to two is the hours with the least frequency.