Averages for Level 2
Averages for Level 2
By the time you have finished this assignment, you will be able to:
• Use the mean
• Use the range
• Use the median
• Use the mode
• Say what an average tells you in a real life situation
Talking About the Range
The range is sometimes called the variation.
What does variation mean?
The range is sometimes called the spread.
What does spread mean?
The range involves finding the difference. What does difference mean?
Let’s put this into a context.
The scores that bricklaying learners get for a diploma test are 4, 6, 9, 3 and 7. The test was out of 10. What does the range tell us about this test?
Find the range for this set of numbers. Show this on a number line like the one you saw earlier:
8, 1, 14, 4, 19
Put the set of numbers into a real life context (story).
What does the range tell you?
Talking About the Mean
To find the mean, we add all of the values up. Next we divide the answer by how many values we had.
Find the mean for 3, 8 and 4.
What was the sum of the 3 items?
What is the sum of the mean average items?
What do you notice about the last 2 answers?
Now put the numbers into a context:
John scores 3 out of 10 for his maths test. Saima scores 8 out of 10 and Adam scores 4 out of 10. What does the mean average of these scores tell you?
To find the mean, we add all of the values up. Next we divide the answer by how many values we had.
Use this box to show finding the mean (just like on the previous page).
Find the mean for £10, £12 and £26.
What was the sum of the 3 items?
What is the sum of the mean average items?
What do you notice about the last 2 answers?
Now put the numbers into a context:
What does the mean average of these scores tell you?
Planters
George the joiner made some garden planters. He showed his new design to some of his old customers. George asked the customers to score the planters out of 10. Here are the scores:
9. 9 8 8 7 9 10 7 8 9
What is the mean average of the scores?
What is the range of the scores?
What does the mean average tell George?
Make a comment.
What does the range tell George?
Make a comment.
George the joiner made another kind of planter. He gave them to 10 customers for free. George asked the customers to score the planters out of 10. Here are the scores:
4 1 3 2 1 0 4 1 4 4
What is the mean average of the scores?
What is the range of the scores?
What does the mean average tell George?
Make a comment.
What does the range tell George?
Make a comment.
How to Find the Median Value
It's the middle number in a sorted list.
Median Value
The Median is the "middle number" (in a sorted list of numbers).
How to Find the Median Value
To find the Median, place the numbers you are given in value order and find the middle number.
Example 1: find the Median of {12, 3 and 5}
Put them in order:
The middle number is ___, so the median is ___.
Example 2
Look at these numbers:
3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
Write the list in order.
Now find the middle number.
Two Numbers in the Middle
BUT, if there are an even amount of numbers things are slightly different.
In that case we need to find the middle pair of numbers, and then find the value that would be half way between them. This is easily done by adding them together and dividing by two.
An example will help:
3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
If we put those numbers in order we have:
There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
In this example the middle numbers are
To find the value half-way between them, add them together and divide by 2:
And, so, the Median in this example is _____
|Averages: Mode |
The mode is a useful type of average as it tells you the number that occurs the most in a set of numbers.
e.g. The mode of {1, 2, 4, 4, 5, 8, 9} is 4 as it occurs the most.
Not every set of numbers has a mode. Furthermore, some sets have more than one mode making its use somewhat limited!
Mode History
Why's it called the mode? The mode is the "most popular" number in a set. The expression comes from the French "a la mode" meaning "fashionable".
Amy has to order boots to use at the centre. She keeps a record of the sizes she has given out in January.
8 9 8 10 12 6 12 11 12 7 5 10 6 8 9 12 6 10 13 9 9
What is the mode?
How do you work out the mode?
Does every set of numbers have a mode?
Does every set of numbers have only one mode?
Where does the word mode come from?
What is the mode for boot sizes?
How can knowing the mode help Amy? Amy looks at the mode and decides to only buy the bigger sizes in future. Is she right?
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Extension
Does it make a difference if you use another average which is not the mean?
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