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Mean and Median
When I first start to teach measures of central tendency and compare mean and median, finding the median can be fun! Some students think that calculating the average and figuring out the mean is just a bit more… mean. But if we do some games and activities, my students start to find the mean and median with their own data, start to see patterns, and have some fun while doing it!
So, to introduce median and mean I get my students up and moving. The first challenge is for them to line up by height. Then students work in stations doing weather research and playing games like Rock, Paper, Scissors, Dice, and Shooting Hoops to find the median and mean of their scores. Students are always motivated to find the mean and the median if there’s a chance it will show their average game score to be the highest in the group!
Set up for the Mean and Median Activity
Have the following materials for stations:
 Dice – at least 6
 Rulers (cm)
 Computers/chromebooks for research
 Empty recycling bin and scraps of paper to make balls
 Selection of pencils of various sizes – at least 9
 Get Your Data In Order worksheet for every student
Set up 5 Stations Around the Room.
You can have duplicate stations depending on your class size.
Station 1: On a roll – 2 dice for every 23 students
Station 2: Measurement – Pencils: 9 different lengths and cm rulers
Station 3: Temperature Research (Tech station)– Computers with weather website for average monthly temperatures. Here is a link to a site where students can search by state
Station 4: Make a Basket – Empty recycling bin and 8 crumpled balls of paper per group
Station 5: Rock, Paper, Scissors (no supplies)
Hand out the worksheet/recording sheet packet to every student.
Have students rotate in groups of 23.
Launch the Lesson on Mean and Median
The students will see that you have stations set up, but before they begin tell them that they have 1 minute to line up. You can have them line up randomly or even ask them to line up in alphabetical order. This is a fun way for students to get moving as soon as they come to your class. Once they are in a line, you might want to take a picture, so they see that they are not in any particular height order. Or choose a volunteer to stand out of the line and be the one who sees the order. Because the next thing they have to do is line up by height.
Using Height as a Data Set
Sixth grade is a great age to use height as a data set, because 11 and 12 year olds all seem to be growing at different rates. You might have students who are as tall as or even are taller than you are, and then there are others who just haven’t reached their growth spurt yet. Plus, they all like to see how tall they actually are. Sometimes you can even get the nurse involved and get some official measurements.
Once the students are lined up by height, point out that they are now in a numerical order. Even if they don’t know how tall they are, they can compare their height to one another. Now ask them who is the tallest? The shortest? Ok. Explain how it is much easier when they are in order to determine those things. Now ask them to figure out who is the middle?
Ah Ha Moment
It’s interesting to watch how students try to figure this out as a group. Because if they move, it makes it harder! Once they think they know the answer, a great way to show them how to strategically find the middle is tell them to all raise their hands high in the air. Then point out the end points again, and tell those two students to put their hands down and cross them in front of their chest. (If they can crouch or sit down, even better). A good way to find the median or middle is to keep crossing out the same number of values from each end. So, now ask the next two end students to put their hands down and cross them. Continue “crossing out” students from each end until…. There’s 1 or 2 people left – in the MIDDLE!. If you have an odd number of people, the MEDIAN or MIDDLE will be one single student. However, if there is an even number of students, crossing out will lead to 2 students standing in the middle. In order to find the median, you can ask students how they would describe the MEDIAN or MIDDLE height when there are two people left. Maybe they are the same height, but if they are different heights then you can show them how to find the height halfway between them. You can do it visually at first, then start getting into calculating this halfway point.
Discussion on Mean and Median
Discuss how the MEDIAN is the MIDDLE person. Take a picture or have students step out and SEE that middle person, with everyone else “crossed out.”
Remind them that their first step is to line up the data from least to greatest, then cross out the numbers to find the middle or median value.
Then talk about the MEAN. This is the calculated average. In order to find the MEAN height, we need to know how tall everyone is. This may need the nurse, or some measuring tapes. If you come prepared with everyone’s height already written down, then you could show how to calculate the mean. If it’s too time consuming, you can have students break up into groups of 5 students. Have them line up and practice finding the median height of their group, then find each other’s heights and calculate the mean height of the group. To find the mean, they must add up their heights, and then divide by the number of people in the group.
Once you’ve done a quick introduction to MEDIAN and MEAN and checked each groups’ calculations, give them each a Get Your Data In Order worksheet and tell them to go with their groups to the stations around the room. Together they will follow the instructions at each station to collect data and find the mean and median.
The Mean and Median Stations
Below are instructions for each station, which are also on the Get Your Data In Order worksheet, which has a page for each station.
Circulate to monitor student work, checking to make sure students are clear between the distinction between median and mean. Ask questions to encourage student discussions about the math concepts they are practicing and to encourage students to extend their thinking.
Station 1 : Roll the Dice
 Roll 2 dice at a time
 Record the sum of the roll in the table on the worksheet
 Do this 7 times
 Once the data is recorded, rewrite it in order from least to greatest
 Find the Median
 Calculate the Mean
 Compare and come up with an explanation for your results
Station 2 : How do the pencils measure up?
 With your partners, each measure 23 pencils to the nearest cm
 Record the measurement in the table
 Rewrite the lengths from least to greatest
 Find the median
 Calculate the Mean
 Compare and come up with an explanation for your results
Station 3 : Temperature Research Station (Tech. need online access)
 Launch the website for climate data
 Pick a state
 Record the average monthly high temperatures by month
 Once the data is recorded, rewrite it in order from least to greatest
 Find the Median (Explain how to find the middle number of 12 data points)
 Calculate the Mean
 Compare and come up with an explanation for your results
Station 4 : Make a basket
 Ball up 7 pieces of paper
 Shoot from a 56 ft away from the recycling bin
 Record how many baskets you make
 Do this 4 times
 Once the data is recorded, rewrite it in order from least to greatest
 Find the Median – explain how you found your middle number (4 trials)
 Calculate the Mean
 Compare and come up with an explanation for your results
Station 5: Rock, Paper, Scissors
 Play rock paper scissors with your partners
 If you win, you get 2 points
 If you lose you get 0
 If you tie you get 1
 Play a round of 5 “shoots”
 Record your score
 Play another round of 5 “shoots”
 Record your score for that round
 Play a total of 5 rounds
 Once the data is recorded, rewrite it in order from least to greatest
 Find your Median score – (for all 5 rounds)
 Calculate your Mean score
 Compare to your partners scores
Reflection on the Data Displays Activity
Each station will have a little bit of competition and a little bit of collaboration. Have students work together and check each other’s work. By comparing scores or comparing the mean to the median in each station, students will start to reflect on their own.
Use the final page of the worksheet to help students reflect on the following questions:
 Why do we have these two ways, Mean and Median, to find an “average” for a set of data?
 When would finding MEAN help describe the data better?
 Why would MEDIAN give a better measure of center?
Relate back to the activity of lining up by height to discuss the advantages of both ways of finding the average. You can also discuss how some data is spread out or has a very high or low extreme. This can affect the mean, but may not change the median at all.
If we replaced one of the shorter heights with a small child, like someone’s little brother or sister, would the MEDIAN person be different? How would it impact the MEAN?
Extensions on Data Displays
 Research and find median and mean for car prices, favorite sports, or other interests. Make a presentation or poster about the data.
 Do jumping jacks or exercises and record your heartbeat/pulse every 20 seconds for the next 3 minutes. Calculate the mean and median heart rate.
FREE Mean and Median Worksheets and Resources
These are all PDF Files. They will open and print easily. The Student Edition Files are labeled SE and the Teacher Editions Files are labeled TE. Click the links below to download the different resources.
 74 Assignment SE – The Mean and Mean Absolute Deviation (PDF)
 74 Assignment TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Bell Work SE – The Mean and Mean Absolute Deviation (PDF)
 74 Bell Work TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Exit Quiz SE – The Mean and Mean Absolute Deviation (PDF)
 74 Exit Quiz TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Guide Notes SE – The Mean and Mean Absolute Deviation (PDF)
 74 Guided Notes TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Lesson Plan – The Mean and Mean Absolute Deviation (PDF)
 74 Online Activities – The Mean and Mean Absolute Deviation (PDF)
 74 Interactive Notebook – The Mean and Mean Absolute Deviation ( Member Only )
 74 Slide Show – The Mean and Mean Absolute Deviation (PDF)
Mean and Median Worksheets and Resources
To get the Editable versions of these files Join us inside the Math Teacher Coach Community! This is where we keep our full curriculum of 4th Grade Math Lessons and Activities.
 74 Assignment SE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Assignment TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Bell Work SE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Bell Work TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Exit Quiz SE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Exit Quiz TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Guide Notes SE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Guided Notes TE – The Mean and Mean Absolute Deviation ( Member Only )
 74 Lesson Plan – The Mean and Mean Absolute Deviation ( Member Only )
 74 Online Activities – The Mean and Mean Absolute Deviation ( Member Only )
 74 Interactive Notebook – The Mean and Mean Absolute Deviation ( Member Only )
 74 Slide Show – The Mean and Mean Absolute Deviation ( Member Only )
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