Stepping into Box Plots
Lesson 4 of 21
Objective: Students will be able to participate in the data collection of a whole class observational study. They will learn about the benefits and pitfalls of displaying data in a box plot and set the stage for motivating future lessons.
As the students enter the classroom, I greet them at the door and ask them to place their back heels against the wall. On the floor, I have taped cm increments. Every student who enters my classroom has his/her feet measured and recorded. To get everyone involved in the data collection, I measure the first person, then have that person measure and record the second person, and so on. This ensures that everyone participates in the data collection. It is really helpful to use an easel to record the data so that you can carry it to the front of the classroom when the students are done!
In this portion of the lesson, I display the data where all students can see it. I ask them what they notice about the data, how it was collected, and what conclusions we may be looking to draw. I also ask them what types of questions they might be interested in investigating about the foot sizes. For example:
1. What is the mean (representative) foot size of the class? What is the median (typical) foot size of the class? What is the shortest foot size in the class? What is the longest foot size in the class?
2. Are there differences in foot sizes for boys and girls? If so, what are the differences?
3. Are foot sizes related to any other variables?
This discussion is usually a really good one! Additional follow up questions: Did any students forget to take off their shoes? What were the pro’s and con’s of having multiple people involved in measuring the data?
I also begin talking to the students about the difference between an observational study and an experimental study. Since nothing was deliberately done to the students, (other than ask them to take off their shoes), this is an observational study. I ask the students for examples of other observational and experimental studies, and we create a list on the board.
In this exit slip, the students will be required to think critically about the benefits and shortcomings of a box plot. They are asked questions that prompt them to view statistics with a well-informed eye! For example, the exit slip figure shows data from two different data sets, each one containing 18 values that vary from 1 to 6 (they are actually histograms, which we will learn about in a later lesson). Data set A has an equal number of values in each group, while Data set B has two peaks at 2 and 5. In other words, the data is symmetric, but their shapes are clearly different. This box plots both look the same! This is because the data sets both have the same five-number summaries — they're both symmetric with the same amount of distance between Q1, the median, and Q3. The students are asked to think critically about his scenario in the exit slip!