The mean, the median and the mode are three different measures of average which we can use. The range is a measure of how spread out data is.
The Mode
The mode is the value that appears most often.
The Median
The median is the middle number (when the numbers are in order).
The Mean
To calculate the mean add up all the numbers and then divide by how many numbers there are.
The Range
The range is the difference between the biggest number and the smallest number.
Example 1: Here are a list of 7 numbers:
7 4 7 9 5 1 2
Find:
a) The mode
b) The median
c) The mean
d) The range
a) The mode is the most common number
The only number that appears more than once is 7
The mode is 7
b) The median is the middle number (but only when the numbers are in order)
We have to put the numbers in order:
1 2 4 5 7 7 9
We can now find the middle number:
The median is 5
c) To find the mean we need to add up all the numbers then divide by how many numbers there are:
1 + 2 + 4 + 5 + 7 + 7 + 9 ⁄7 = 35⁄7 = 5
The mean is 5
d) To find the range we take the smallest number away from the biggest number
9 - 1 = 8
The range is 8
Example 2: Here are a list of 8 numbers:
6 6 13 5 11 11 11 9
Find:
a) The mode
b) The median
c) The mean
d) The range
a) The mode is the most common number
11 appears three times, that is more than any other number
The mode is 11
b) To find the median (the middle number) we need to put the numbers in order:
5 6 6 9 11 11 11 13
We can see that there is not one middle number, we have 9 and 11 in the middle.
When this happens the median is half way between the two middle numbers, the middle of 9 and 11 is 10. We can work this out by adding 9 and 11 and then dividing by 2.
9 + 11⁄2 = 10
The median is 10
c) To find the mean we need to add up all the numbers then divide by how many numbers there are:
5 + 6 + 6 + 9 + 11 + 11 + 11 + 13⁄8 = 72⁄8 = 9
The mean is 9
d) To find the range we take the smallest number away from the biggest number
13 - 5 = 8
The range is 8
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