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How to Make a Frequency Histogram

Instructor: Nick Rogers
Frequency histograms are a type of graph that allows us to easily compare categories or ranges of data. They are easy to read and construct and can be a great tool for you to display statistics.

Histograms

Have you ever seen a histogram? A histogram is a popular graph used in statistics. The vertical axis shows how much of something that you have, and the horizontal axis labels the categories that you are plotting. For example, if your class consisted of 12 boys and 10 girls, you'd plot a histogram of the students as follows:

Traditional histogram (left) vs. a frequency histogram (right)
Traditional and frequency historgrams

On the left of the diagram is a traditional histogram: it displays the number of boys and girls in the class. To the right is the same data plotted as a frequency histogram. You calculate the frequencies by comparing the number of boys and girls to the total number of students. How can you calculate the frequency of girls and boys in the class? You can do this by using fractions of the total number of students. There are 12 boys and 10 girls, so there are 22 students total.

Calculating Frequencies

Let's calculate the frequencies:

  • Girls / Students = 10 / 22
  • Girls / Students = 0.45
  • Boys / Students = 12 / 22
  • Boys / Students = 0.54

Therefore, the frequency of girls in the class is 0.45 or about 45%. Similarly, the frequency of boys is 0.54 or 54%. It is very useful to consider frequencies when drawing these kinds of graphs because frequency is never more than '1.' What other kinds of things can you measure with these plots? Almost anything!

Sample Plots with Data

Let's try to make some plots using data. Imagine that you asked everyone in your class what their favorite color is. You collect all of the answers in a list:

(blue, yellow, green, blue, red, blue, yellow, green, blue, red, green, blue, red, blue, yellow, yellow, green, blue, blue, red, purple, orange)

This list is a little hard to read, so one way we can make it easier to understand is to arrange it into a nice table:

Color Number Frequency
Blue 8 0.36
Red 4 0.18
Yellow 4 0.18
Green 4 0.18
Purple 1 0.18
Orange 1 0.045

Now that we can see all of the data in a table, we find that blue is the most popular color, followed by red, yellow, and green; purple and orange were the least popular. This certainly helps our understanding, but can you create a histogram from this data? A histogram may look like this:

Histogram of favorite colors
A Histogram of Our Example - Favorite Colors

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