Mean, Median, Mode
Introduction
If you are given a set of numbers such as the test scores of 10 students: 34%, 44%, 75%, 21%, 98%, 86%, 71%, 76%, 63% and 55%.
What useful calculations can you perform to the numbers? Hint: This song may refresh your memory of what they are and how to calculate them.
What do these calculations tell you?
What are the advantages and disadvantages for each of these calculations?
Support
Some useful calculations are mean, mode, median and range. If you need to, you are encouraged to look at the relevant skills on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit. The skills that you will need are:
K236: "Find the mean of listed data."
K239: "Find the range of listed data."
K240: "Find a missing item given the mean and the other items."
K243: "Determine the resulting mean when a value is removed."
K237: "Find the mode of listed data."
K238: "Find the median of listed data."
K241: "Determine a list of integers given information about their mean, median, range and mode."
K242: "Determine the value that resulted in a change of mean."
K244: "Determine the combined mean of two groups."
K245: "Determine the mean of one group given the combined mean and the mean of the other group."
Transum
Practise finding averages with the task and game below:
Averages: Test your understanding of averages with this self marking quiz about mean, median and range.
Choose Your Average: This is a game for two players. You should know how to find the mean, median and range of a set of numbers.
MMM
Take a look at the following problem from nRich. There are several sets of five positive integers (whole numbers) with the following properties:
Mean = 4
Median = 3
Mode = 3
Can you find all the different sets of five positive whole numbers that satisfy these conditions?
How many answers are there?
How can you be sure that you have found them all?
Now repeat for the following questions:
Extension
Below are more challenges to do with averages!
Here's an interesting set of five numbers: 2, 5, 5, 6, 7
The mean, mode, median and range are all 5.
Can you find other sets of five positive whole numbers where:
Mean = Median = Mode = Range
Mode < Median < Mean
Mode < Mean < Median
Mean < Mode < Median
Mean < Median < Mode
Median < Mode < Mean
Median < Mean < Mode
Not all of these can be satisfied by sets of five numbers! Can you explain why?
Show that some of them can be satisfied with sets of just four numbers.
Show that all of them can be satisfied with sets of six numbers.
Take the numbers 1, 2, 3, 4, 5, 6 and choose one to wipe out.
For example, you might wipe out 5, leaving you with 1, 2, 3, 4, 6. The mean of what is left is 3.2.
Can you wipe out one number from 1 to 6, and leave behind five numbers whose average is a whole number?
How about starting with other sets of numbers from 1 to N, where N is even. If you are to wipe out just one number, which number you should wipe out so that the mean of what is left is a whole number? Can you explain why?
Now repeat the same thing with other sets of numbers from 1 to N, where N is odd? Are there any interesting patterns?
Here are some puzzling wipeouts you might like to try:
One of the numbers from 1, 2, 3, 4, 5, 6 is wiped out. The mean of what is left is 3.6. Which number was crossed out?
One of the numbers from 1, 2, 3, 4, 5, 6, 7 is wiped out. The mean of what is left is 4.0. Which number was crossed out?
One of the numbers from 1 to 15 is wiped out. The mean of what is left is 7.714285714285... Which number was crossed out?
One of the numbers from 1 to N, where N is an unknown number, is wiped out. The mean of what is left is 6.83333... What is N, and which number was crossed out?
One of the numbers from 1 to N is wiped out. The mean of what is left is 25.76. What is N, and which number was crossed out?
C: The Ice Cream Problem
What if…
The person at 5m decided it was too noisy and moved to 15m?
Then another person arrived and sat at 12m?
D: Transum
Here are some puzzles/ starters on averages from Transum:
Five Digits: Five digits have the same mean, median, mode and range.
House Numbers: The numbers on five houses next to each other add up to 70. What are those five numbers?
Cube Ages: Calculate the mean age of the two fathers and two sons with the given clues.
E: Don Steward
Don Steward has written a lot of excellent questions here. For a sample take a look at the questions below:
