In the Introduction of this lesson, I have students compare seven different test scores of two different students. I hand each student a copy of the Introduction to work individually. Due to lack of space on the page, students should complete the Introduction on their own paper. I am using the Introduction to access the students' prior knowledge. This should be review for most of the students. I expect the Introduction to take about 25 minutes for the students to complete and for me to review with the class. The time for this activity may vary depending on the level of your students.
Students are to look at the two data sets of test grades and determine the Central Tendencies. Students then are to determine which Central Tendency that each student would want to represent their test scores. The two students given, Peter and Amulet, want the highest percentage to represent their test scores.
Peter will want the mean of 86 to represent his test scores compared to the median and mode of 84 in his data set. Amulet will want the median or the mode of 84 to represent her test scores. The mean of Amulet's scores is 82, and would make her test scores look lower. Both students scored an 84 twice on a test, and therefore had the same mode.
The second question of the introduction has students create a summary of the data of cell phone usage given using a Box and Whisker Plot. The final question asks students to explain the process of creating a histogram for the same set of data used for question two. Students do not have to create the histogram, but just explain the process.
I demonstrate reviewing parts of the Introduction in the video below.
After reviewing the Introduction with the students, I hand each student a page to take Notes on as I present a Power Point. The Power Point is on the Advantages and Disadvantages of Dot Plots, Box Plots, and Histograms. The information that I review in the Warm Up helps students identify these Advantages and Disadvantages as well.
Below, I have listed some possible notes for students on each section:
1. Dot Plots
2. Box Plots
The students notes may vary. If given numerical data, all of the three graphs are an option. In this lesson, I am trying to present to students which one of the graphs is the best option.
After students finish viewing the Power Point and taking Notes, I hand each student an Exit Slip with about 10 minutes remaining in the period. I use the Exit Slip as a quick formative assessment to check for the ability of each student to select the best graph possible for a set of data. Student are to hand in the Exit Slip before leaving.
In the Exit Slip, I provide students with a set of data representing the number of miles that 20 people travel to work. Several of the students chose the Dot Plot because I think it is the easiest graph to create. However, one of the benefits of using the Dot Plot is that you can see every data point. This is a data set of 20, and the Dot Plot should be used for a small data set. So, this data set is almost too large to use for a Dot Plot.
The Box Plot shows a visual summary of the data, but it is difficult to conclude anything about the data from this graph. When analyzing the graph, fifty-percent of the data points of miles traveled was between 3.5 to 13.5 miles. However, this does not really provide much insight about how many miles people travel to work. Providing other percentages about the Box Plot is also of little help.
The Histogram is the best option if the reader is looking for the miles traveled to be summarized into intervals. The highest bar in the graph represents the mode of the data. When using an interval of three for each bin, it shows that the most common miles people traveled to work is either 0-3, 3-6, or 6-9. The range of the miles traveled to work was one to eighteen miles. There was no person that traveled ten or eleven miles.
I show some of the reasoning on selecting the best graph to represent the data given in the video below.
After reviewing the different characteristics of each type of graph with students, we come to the conclusion that selecting a graph also depends on what part of the data the reader wants to highlight.