Mean, Median, Mode and Range – known collectively as MMMR – are the basic statistical functions that you need to know for National 5 Maths. The two more advanced concepts are (Semi) Interquartile Range and Standard Deviation. IQR and IQR are covered here, Standard deviation will get a page to itself.
Mean
The mean is often called the ‘average’, though perhaps avoid that – the median is also sometimes called the average, so it can get confusing. One way of thinking about the mean is as ‘sharing out’.
To find the mean, add all the numbers and divide the total by how many numbers you started with. For example:
Find the mean of:
2,8,10,1,9
2 + 8 + 10 + 1 + 9 = 30
30 ÷ 5 = 6
Mean = 6
In this case, you can imagine five people who have 2, 8, 10, 1 and 9 bananas (or whatever). If they put them in a pile and share them out, each will get six bananas.
Sometimes people get fractions of a banana:
Find the mean of:
7, 2, 3, 6
7 + 2 + 3 + 6
18 ÷ 4 = 4 1/2
Mean = 4 1/2
When there are negatives it makes less sense to think of ‘sharing out’, but the maths is the same:
Find the mean of:
1, 2, -5, 1, 7, 6
1 + 2 - 5 + 1 + 7 + 6 = 12
12 ÷ 6 = 2
Mean = 2
Median
The median is the middle – the words sound a bit alike which helps you remember them. Unlike the mean, before you do the median you must put the numbers in order. Then, if there are an odd amount, pick the middle one:
Find the median of:
3, 7, 1, 5, -2
Put the numbers in order:
-2, 1, 3, 5, 7
Middle number = 3
Median = 3
If there are an even amount of numbers, the median is half way between the two central ones:
Find the median of:
9, -2, 10, 6, 2, 0
Put the numbers in order:
-2, 0, 2, 6, 9, 10
Central two numbers are 2 and 6. Half way between these is (2+6)/2 = 4
Median = 4
Mode
This is probably the easiest of the four. Mode just means the number that occurs most often (MOde = MOst):
Find the mode of:
4, 1, -8, 7, 4, 2, 7, 4, 1
There are three 4s, more than any other number, so Mode = 4
Range
The range is simply the biggest number minus the smallest. You don’t have to put the numbers in order to work this out, but it can help you avoid missing any:
Find the range of:
3, 7, 10, 11, -3, 2, 8, 11
Highest = 11, Lowest = -3
11 - -3 = 11 + 3 = 14
Inter Quartile Range
The inter-quartile range (IQR) and semi inter-quartile range are mainly used in the statistics topic, but it makes sense to discuss them here.
To find the interquartile range, first find the median (sometimes called the second quartile, or Q2). Then find the median of the values lower than this (Q1) and the median of the values higher than this (Q3). The IQR is the difference between Q3 and Q1. The SIQR is half of the IQR. Here’s an example:
5,7,7,9,12,14
The numbers are already in order, so the median is in the middle: half way between 7 and 9 = 8.
To find Q1, we find the median of 5,7,7 which is 7. Q3 is the median of 9,12,14 which is 12. So the IQR is 12 – 7 = 5 and the SIQR is 5/2 = 2.5