Analyze this! Mean Median Mode and Range

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Objective

The students will be able to understand how to calculate the measures of central tendency and be able to use it to describe the data.

Big Idea

Finding measures of central tendency will be applied to the different graphs throughout this unit

Understanding Mean

15 minutes

You can use counter chips to find a single number to describe the data set.

First, use counters to make stacks that match the data (power point)

Next, have the students move the counter chips so that all stacks are the same height.

Finally, all the stacks have 4 counter chips.  The set of data can be described by the number of counter chips (4).  This is called the mean or the average.

Show the students the next table and have them find the mean in the same way. Have the students discuss their results with their tablemates.

 Think and discuss

  • Suppose one person surveyed had 8 brothers and sisters.  How would this affect the mean?
  • All of the students in class have 3 pets. What is the mean of this data set?  How do you know?

Tools: counter chips or other stackable item

Understanding Vocabulary and How to use it to Calculate Measures of Central Tendency

55 minutes

The middle part of this lesson is dealing with the vocabulary and calculating the measures of central tendency.  The focus on the vocabulary is to not only get the students to be able to calculate the measures of central tendency but to also know which measure of center would be best to use when given different data sets.  Allow the students to complete the vocabulary notes in their charts before beginning the whole group discussion.  I like to sing them a song that helps them to remember which measure of center measures what.  Once the students are done with the vocabulary, give them some time to “quiz” each other over their meanings.  It would be best to use the game like catch phrase to help with internalizing the meaning of the words.  For example, students wouldn’t just read the definition to the partner.  They could act it out, use gestures or use their own words to get their partner to say the correct word.  The students then would switch roles.  (10 minutes). Bring students back and start working on calculating mean, median, mode and range.

The power point is set up so that there is one problem to do together and the other for them to work on independently. The actual problems were used to represent real life situations.  As students work on the problems independently, I would have them share with a table mate to discuss their strategy and justify their answer (MP6)(MP3)

Next, to allow students to practice their new knowledge, have them work together in a group called show down. 

  • Each group gets a stack of cards
  • One person is the show down captain. (the showdown captain turns over the card and calls “show down” when all group members have completed the problem.)
  • Each person in the group works on the problem independently.  They can turn their boards over to show they are ready to move on.
  • Once everyone in the group is done, the captain calls “show down” and all team members turn their boards over to reveal their answers.
  • Group members look over each other’s answers, discuss, and congratulate when all have the correct/same answer.
  • The team captain job rotates and the process starts over again. 

During this time the teacher’s role changes from teacher to facilitator.  This activity allows the teacher to move around to the different groups to assess understanding of the concepts learned. 

Bring the group back for closure.

Tools: white boards and markers

Closure

10 minutes

Have students reflect on their learning in their journal or out loud. Today we learned how to calculate the mean, median, mode and range of a set of data. We also looked at outliers and how they affect our data set. 

 How is the range affected by an outlier? Give an example to justify your answer

Give a data set that has the same mean, median and mode? 

I chose these two questions to extend their learning for the day.  Today they have been working the calculations (naked math)but the goal is to get them to think about numerical data sets and all of its values and how it varies by changing the numbers.