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In Chapter 7, you studied both histograms and bar graphs. Remember that histograms have measurements on the horizontal axis (x) and frequencies on the vertical axis (y). A bar graph, on the other hand, displays categories on the horizontal (x) axis and frequencies on the vertical (y) axis. This means that bar graphs are more qualitative, and, therefore, display categorical data. The figure below shows 1 bar graph (on the top) and 1 histogram (on the bottom):

Let’s look at an example of double bar graphs.

Example 8

Kerry-Sue is surveying a random sample of students to determine which sports they would like to have set up at the end-of-year Safe Grad event. She collects the following data:

Sports Girls Boys
Racquetball 6 3
Basketball 3 6
Volleyball 5 5
Swimming 7 8

Draw a double bar graph and help Kerry-Sue determine which 2 sports would be most equally-liked by both boys and girls at the end-of-year Safe Grad event.

Solution:

According to the double bar graph, volleyball and swimming seem to be almost equally liked by both the girls and the boys. Therefore, these 2 sports would be the ones Kerry-Sue should choose to set up at the end-of-year Safe Grad event.

Example 9

Mrs. Smith teaches both academic and advanced math. She has been teaching these 2 courses for the past 4 years. She decided she wanted to compare her grades to see how each class was doing over the past few years and see if she has improved her class instruction at all. Her data can be found below:

Marks Academic Math Advanced Math
2007 61.3 74.7
2008 67.9 80.3
2009 50.9 86.8
2010 63.7 81.5

Draw a double bar graph and help Mrs. Smith determine if her class instruction has improved over the past 4 years.

Solution:

Both the academic and advanced math marks went up and down over the past 4 years. If Mrs. Smith looks at the difference between 2007 and 2010, she can see that there is an improvement in the final grades for her students. Although there are many factors that can affect these grades, she can say that the change in her instruction is making some difference in the results for her students. Other factors might have contributed to the huge decline in grades for the academic math students in 2009. You can make this conclusion for Mrs. Smith, as there was a marked improvement in her advanced math course. In 2009, it seemed her instruction methods were working well with the advanced students, but other factors were affecting the academic students.

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