I begin class by letting students know that today they will begin a new unit on Statistics. I write the word "statistics" up on the board and ask students what they know about the topic. Students should have had exposure to statistics beginning in Grade 6, so they may be able to share a lot of what they have learned.
Teacher's Note: I work specifically with students who have had interruptions to their education and/or have struggled academically, so this lesson is intended to cover the basics about representing data. Because it may be a review for some students, there are opportunities for them to be the teachers in the next lesson.
To begin, I share with them some formal definitions of statistics. I like the way the Common Core Standards introduces the topic:
Decisions or predictions are often based on data—numbers in context. These decisions or predictions would be easy if the data always sent a clear message, but the message is often obscured by variability. Statistics provides tools for describing variability in data and for making informed decisions that take it into account (High School Statistics and Probability, accessed August 19 2014).
I tell students that Statistics is a very practical math topic and they will encounter statistics throughout their lives. Statistics can also be used in more playful contexts. I ask if anyone has seen the movie Moneyball. If anyone has, I ask if they can explain the basic premise of the movie. I then show students the following clips from the film, pointing out the use of statistics where it arises.
The trailer: This clip gives a good overview of the film and the method
Source: YouTube (accessed August 19, 2014)
A specific scene about using statistics in baseball:
Source: NY Times (accessed August 19, 2014)
And finally, a behind the scenes look:
Source: YouTube (Accessed August 19, 2014)
I tell students that this way of looking at player performance and analyzing a variety of statistics has changed the game of baseball and the way teams are put together. I tell students that today they will begin to collect and look at some data about themselves and think about ways to describe the data.
In today's activity, students will collect data about themselves by taking their pulse (see Describing Data Video). I show students how to take their pulse and may have to help some students find their pulse on their wrist.
This YouTube video gives a good description of the process:
Source: YouTube (accessed August 19, 2014)
I like to do this as a whole group activity because the timing and counting requires a quiet room. I lead the students in taking their pulse 10 times each for a count of 15 seconds. I tell students to begin their pulse count at "0."
Once students have recorded 10 different 15-second intervals, I break them into groups of 4 and ask them to share their data. Each student should have a record of the group's results. I ask each group to describe their data. I tell them to imagine they were going to share their data with another group, but they would have to describe the data, not just give the other group their list.
In what ways could they give a description of what the data was like?
The students I work with often have difficulty with this task. Most groups begin to describe the data using the range, but then seem stuck after that. In a sense, this is a positive, because it draws them into the skills they are about to learn next and shows them the usefulness of describing data in different ways. I push them here though to think of some ways to describe the data beyond using just the range. I keep returning to the idea of telling someone else about the data set without using the actual number.
How could they begin an accurate description?
I also might ask them if they can think of a way to represent the data visually.
At the end of class, I let students share out how they would describe their data. There are no right or wrong answers here, but I do want to begin to highlight some key points. Students will likely have used concepts like range, mean, and perhaps even median and mode if they remember or have exposure to previous work with data. I clarify each of these terms for the class and I make sure everyone understands their definitions.
I often spend some time brainstorming with students about the difference between the median and mean in terms of what it tells you about that data (not necessarily how you calculate it). We talk about outliers and measurement variation versus students having different pulses. I ask if any groups were able to represent the data visually? If a group has done so, they share out their work. If not, I ask the class about some ways they could represent the data visually. I try to elicit ideas about histograms, box plots, and dot plots.
I let students know that tomorrow, they will be creating different ways to look at this data so it is important that they save their work. They will compare the results of the of different methods and discuss the advantages and disadvantages of the visuals.
In closing, I ask students to return to the initial introduction to statistics at the beginning of the class. I ask them to write an Exit Ticket reflection:
Describe where you see statistics in use in your every day life.