Histograms Examples

Create a histogram displaying the top ten women's figure skating scores for the 2010 Winter Olympics

The x-axis needs to span from at least 171 to 229 in order to accommodate all of the data.

Since we are not given a specific bin width we can create a histogram with whatever width we choose. It is easiest to pick a nice round number like 5 or 10, but it really depends on how the data is spread. We choose a bin width of 10 points.

Now we look at the data and find how many skaters scored in each interval. The highest will be 180-190, with a frequency of 4, so we need to make sure that our y-axis spans to at least 4.

Finally we plot the frequency of each interval: 2 between 170-180, 4 between 180-190, 1 between 190-200, 2 between 200-210, and 1 between 220-230.

This histogram represents the scores from the last geometry test. They are graphed with a bin width of 7.

a) How many students took the test?

To find the total number of students, we need to add the number of times each score occurs (each score's frequency).

Total = 1 + 4 + 2 + 3 + 4 + 1 = 15 students

b) What percentage of students scored above 78?

To find the percentage we need to divide the number of students who scored above 78 by the total number of students (15). 8 students scored above 78 (add up the last three bars).

c) Which interval contains the median?

Since there are 15 scores, the median (middle) score will be the 8th score. This will be located between 178-185.

How many students scored below 60 points on the histogram in Example 2?

There is only one column on the histogram below 60 points, and its frequency is 1 so only 1 student scored below 60 points.