Averages Summary
Description / ModeThe one there’s MOST of / Median
Put them in order then find the MIDDLE one / Mean
Add them all together then divide by how many numbers there are / Range
Subtract the smallest from the biggest
From a LIST
14 14 15 16 16 16 17 17 18 19 20 / 16 /
14 14 15 16 16 16 17 17 18 19 20 / 182 ÷ 11 = 16.5 / 20 – 14 = 6
From a DISCRETE (exact) frequency distribution / 2
Looking at the frequency column there are nine 2’s – more than any other number. / 2
Adding the frequencies tells us that there are 23 numbers in total. So the 12th number is the median- you could include a cumulative frequency column to make this easier to find. / 48 ÷ 23 = 2.09
Create an fx column, add them together then divide by the total frequency (f),
(this is because there are:
two 0’s, five 1’s nine 2’s etc). / 5 – 0 = 5
From a GROUPED frequency distribution / 5-9
Is the modal class
The biggest number in the frequency column is 71 – that is the 5-9 group or class. / 5-9
Adding the frequencies tells us that there are 150 numbers in total. So the 75.5th number is the median- this comes in the 5-9 group. You could include a cumulative frequency column to make this easier to find. / 1325 ÷ 150 = 8.83
As above we need an fx column, but first we need to create an x column by finding the mid-points (add the 2 numbers then divide by 2, e.g. 5+9=14, 14÷2=7) / 24 – 0 = 24
The shaded parts of the tables show the things you need to work out and fill in yourself. fx means f×x
H Jackson 2010-14 / Academic Skills 1