Mean, Median, Mode and Range from Dot Plots Lesson Plan

Warm-up

Have students work on a warm-up activity reviewing finding mean, median, mode, and range of a set of numbers. Hand out one copy to each student and give them a few minutes to work.

Let students share their answers with the class and then go over any missed answers so that all students can review how to find mean, median, mode, and range.

Tell students that they are going to be working with dot plots today to find the mean, median, mode, and range.

Notice and Wonder

Start the lesson by displaying slide one of the teacher slideshow. Have students do a notice and wonder of what they see.

Give students a few minutes to come up with a list of things that they notice and wonder about the dot plot. They can share with a partner before you begin a class discussion. 

Answers to look for:

• Possible noticings
  • `2` students spent `0` hours on homework
  • The most students spent `8` hours on homework
  • `0` students spent `2`, `4`, and `10` hours on homework. 
  • `3` students spent `1` hour and `5` hours on homework
  • The title is “How many hours…
  • The number line is numbered from `0` to `10`
• Possible wonderings:
  • Why did no students spend `2` hours on homework?
  • Why is it numbered `0` to `10`?
  • What do the “`x`’s” represent?

Notice and Wonder Discussion

Once students have shared their notices and wonders, share any of the above ones that may not have been brought up. Ask questions like “How many students were there in all? How do you know?” Tell students that they will use these dots plots to find the mean, median, mode, and range. Let them know that we can do this by listing the data from the dot plot.

Listing the data points

Advance to slide `2` and review with students how to list the data from a dot plot. You’ll want to start on the left so that we can encourage students to write the data in order from least to greatest.

Start by asking a question about the first number like, “how many students spent `0` hours on homework each week?” When students answer `2`, you should ask them what we should write as the data point. Some students are likely to answer `2` while some others might think that you should write `0` two times. Have a conversation around this. Ask them how many data points do you expect to write? How many students were part of this survey? Continue in a similar way until you’ve listed all the data from least to greatest.

Finding the mean

Show the next dot plot on slide `3` and remind students that finding the mean is the same as finding the average. Ask students what they think is the mean of the data - can they figure it out visually? See if students can think of the mean while looking at the distribution of the dots. Even if they are not close to the actual answer, it is useful to start thinking of the mean visually.

We have already looked at how to find the mean in the review. Ask students to find the mean. Let students share the ways in which they added the data points - hopefully some students will share that they did `1 + 3 + (3\times 5) + 6 + (4\times 8) + 9`. Talk about why you can do this in a dot plot.

Finding the median

Ask students to find the median of the data given in the dot plot. As students share their strategies it will be interesting to see that some students will use the list of the data points while some might prefer to cancel the dots from both sides - or some might just count up to half the number of dots.

Finding the mode

When you ask students to find the mode, they might conclude that the  number that has the most dots above it is the mode. Remind students that there can be more than one mode. For example, if two numbers had `4` dots above them in this dot plot.

Finding the range

Finding the range with dot plots can also be helpful to do visually. Students might conclude that they just have to look at the greatest number and the smallest number with at least one dot  - a common misconception is to look for the greatest and smallest numbers on the number line without checking whether there are any dots above the numbers. 

Partner Activity

Pass out the partner activity where students will sort cards with the correct dot plot. Explain to students that there will be `4` dot plots and then a variety of numbers that could be the dot plots mean, medians, modes, or ranges. Students will need to sort the numbers with the correct dot plot.

The answer key is attached as well.