WJEC MATHEMATICS
INTERMEDIATE
STATISTICS AND PROBABILITY
AVERAGES AND RANGE
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Contents
Mode
Median
Mean
Range
Working Backwards
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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There are three types of average: mode, median, and mean.
Depending on the circumstances one of these may be better to look
at than the others.
Mode
The mode of a set of a numbers is the number that appears the
most
Example 1
Find the mode of the following
In the above list, the number 5 appears more than any other, so in
this example mode = 5
Example 2
Find the mode of the following
In the above list, the number 5 and the number 1 appear more than
any other, so in this example mode = 5 and 1
Example 3
Find the mode of the following
In the above list, no number appears more than any other, so there
is NO MODE
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Exercise S6
Calculate the mode of the following sets of numbers
a.4,5,3,2,1,4,1,4
e.12,15,12,16,15,15,17
b. 3,3,5,6,4,1,2,3,5,1
f.4,5,8,6,2,5,1,4,5,2,6,3,2,1,2,1,
c.2,3,4,2,3,6,8,5,9
g.102,201,202,101,120,210
d.12,16,15,21,14,18,19
h. 1,3,2,2,5,4,2,21,3,3,5,4
Median
The median is the middle number in a list of numbers that has been
put into order from the smallest to largest. Sometimes there will be
two numbers in the middle (if the list has an even amount of
numbers). If this is the case, add the two middle numbers up and
divide the answer by 2.
Example 1
Find the median of the following set of numbers
Step 1
Put the numbers in order
Step 2
Cross numbers off from each end until you are left with one or two
numbers in the middle
Median = 4
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Example 2
Find the median of the following set of numbers
Step 1
Put the numbers in order
Step 2
Cross numbers off from each end until you are left with one or two
numbers in the middle
Step 3
As there are two numbers in the middle we have one extra step add them up and divide by 2.
So Median = 6
Exercise S7
Calculate the median of the following sets of numbers
a.4,5,3,2,1,4,1,4
e.12,15,12,16,15,15,17
b. 3,3,5,6,4,1,2,3,5,1
f.4,5,8,6,2,5,1,4,5,2,6,3,2,1,2,1,
c.2,3,4,2,3,6,8,5,9
g.102,201,202,101,120,210
d.12,16,15,21,14,18,19
h. 1,3,2,2,5,4,2,21,3,3,5,4
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Mean
To find the mean from a list of numbers we need to add them up to
get a total and then divide the topic by how many numbers are in the
list
Example 1
Find the mean of the following set of numbers
Step 1
Add up the numbers to get a total
Step 2
Divide the total by how many numbers there are in the list
Exercise S8
Calculate the mean of the following sets of numbers
a.4,5,3,2,1,4,1,4
e.12,15,12,16,15,15,17
b. 3,3,5,6,4,1,2,3,5,1
f.4,5,8,6,2,5,1,4,5,2,6,3,2,1,2,1,
c.2,3,4,2,3,6,8,5,9
g.102,201,202,101,120,210
d.12,16,15,21,14,18,19
h. 1,3,2,2,5,4,2,21,3,3,5,4
Which Average to use?
Depending on the data, one of the above averages may not be the
best to use. For example, if the data are
The mean would be 18 which doesn't reflect these numbers. In this
case median, or even mode, would be better.
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Range
To find the range of a list of numbers, subtract the smallest number
from the largest number
Example
Find the range from the following list of numbers
Exercise S9
Calculate the range of the following sets of numbers
a.4,5,3,2,1,4,1,4
e.12,15,12,16,15,15,17
b. 3,3,5,6,4,1,2,3,5,1
f.4,5,8,6,2,5,1,4,5,2,6,3,2,1,2,1,
c.2,3,4,2,3,6,8,5,9
g.102,201,202,101,120,210
d.12,16,15,21,14,18,19
h. 1,3,2,2,5,4,2,21,3,3,5,4
Working Backwards
Sometimes we are given the value of the averages and asked to find
the numbers. Here's a quick guide for those questions.
Example
The mean, median, mode, and range of five single digit numbers is
5. Write a combination of 5 numbers that satisfy this.
Step 1
Begin with the median as this value can be immediately placed.
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Step 2
The range needs to be 5 so select two single digits that subtract to
give 5
Step 3
For a median of 5 we need more 5's than any other number
Stage 4
For the mean of these numbers to be 5, the numbers need to add up
to 25. So the missing number must be;
1.
Exam Questions S9
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