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The mean, median and mode are types of average.
The range gives a measure of the spread of a set of data.
This section revises how to calculate these measures for a simple set of data.
It then goes on to look at how the measures can be calculated for a table of data.
Calculating the Mean, Median, Mode and Range for simple data
The table below shows how to calculate the mean, median, mode and range for two sets of data.
Set A contains the numbers 2, 2, 3, 5, 5, 7, 8 and Set B contains the numbers 2, 3, 3, 4, 6, 7.
Measure Set A
2, 2, 3, 5, 5, 7, 8 Set B
2, 3, 3, 4, 6, 7
The Mean
To find the mean, you
need to add up all the
data, and then divide
this total by the number
of values in the data. Adding the numbers up gives:
2 + 2 + 3 + 5 + 5 + 7 + 8 = 32
There are 7 values, so you divide
the total by 7: 32 ÷ 7 = 4.57...
So the mean is 4.57 (2 d.p.) Adding the numbers up gives:
2 + 3 + 3 + 4 + 6 + 7 = 25
There are 6 values, so you divide
the total by 6: 25 ÷ 6 = 4.33...
So the mean is 4.33 (2 d.p.)
The Median
To find the median, you
need to put the values
in order, then find the
middle value. If there are
two values in the middle
then you find the mean
of these two values. The numbers in order:
2 , 2 , 3 , (5) , 5 , 7 , 8
The middle value is marked in
brackets, and it is 5.
So the median is 5 The numbers in order:
2 , 3 , (3 , 4) , 6 , 7
This time there are two values in
the middle. They have been put
in brackets. The median is found
by calculating the mean of these
two values: (3 + 4) ÷ 2 = 3.5
So the median is 3.5
The Mode
The mode is the value
which appears the most
often in the data. It is
possible to have more
than one mode if there
is more than one value
which appears the most. The data values:
2 , 2 , 3 , 5 , 5 , 7 , 8
The values which appear most
often are 2 and 5. They both
appear more time than any
of the other data values.
So the modes are 2 and 5 The data values:
2 , 3 , 3 , 4 , 6 , 7
This time there is only one value
which appears most often - the
number 3. It appears more times
than any of the other data values.
So the mode is 3
The Range
To find the range, you
first need to find the
lowest and highest values
in the data. The range is
found by subtracting the
lowest value from the
highest value. The data values:
2 , 2 , 3 , 5 , 5 , 7 , 8
The lowest value is 2 and the
highest value is 8. Subtracting
the lowest from the highest
gives: 8 - 2 = 6
So the range is 6 The data values:
2 , 3 , 3 , 4 , 6 , 7
The lowest value is 2 and the
highest value is 7. Subtracting
the lowest from the highest
gives: 7 - 2 = 5
So the range is 5
:Dvery good
:Dvery good
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