Statistics Explained

Beginners:Statistical concept - Mean and median

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This page is part of Statistics 4 beginners, a section in Statistics Explained where statistical indicators and concepts are explained in an simple way to make the world of statistics a bit easier both for pupils and students as well as for all those with an interest in statistics.

An average can be described as a summary of a group of numbers as a single number. There are different types of averages; the most common used in official statistics are mean and median.

Mean

The mean (also called arithmetic mean), in everyday language called the average, is the sum of the values of a group of numbers divided by the amount of numbers in the group.

Example

We have 9 numbers in a group: 10, 12, 11, 15, 13, 35, 41, 23, 20. The sum of these 9 numbers is 180. Then the sum of 180 is divided by 9 in order to get the average. The average is 180/9 = 20.


In official statistics, the most common type of average is the weighted average or weighted mean, as it is rare that all items have the same importance. In a weighted average, each item taken into account is multiplied by a number (weight), which reflects the item's relative importance, then the result is added up before being divided by the number of items.

Example

Population % not owning a car
Country A 20 million 5%
Country B 500 thousand 30%
Country C 1 million 16%
Total A+B+C 21.5 million This is a weighted average – how is it calculated?

The average of those not owning a car in these 3 countries is NOT calculated by adding 5% + 30% + 16%=51% and then 51%/3=17% since the different size of the 3 countries has to be taken into consideration. The weighting factor in this example is the population.

The way to calculate the weighted average is:

5 % of 20 million = 1 million

30 % of 500 thousand = 150 thousand

16 % of 1 million =160 thousand

Total: 1 million + 150 thousand + 160 thousand = 1.31 million

The weighted average is [(1.31 million/21.5 million) -1] x100 = 6 % (rounded)

Median

The median is the middle value in a group of numbers ranked by size. It is the number which is exactly in the middle so that 50% of the ranked numbers are above and 50% are below the median.

Example

In order to find the median of the same 9 numbers: 10, 12, 11, 15, 13, 35, 41, 23, 20, first put them in ascending order, i.e. 10, 11, 12, 13, 15, 20, 23, 35, 41 - the middle number is 15: the median is 15 as 4 numbers are below 15 and 4 numbers are above 15.

If there is an even amount of numbers: 10, 11, 12, 13, 15, 20, 23, 35 - the two in the middle (13 and 15) are added together (13+15=28) and then divided by 2 (28/2= 14), which means the median in this case is 14.

Further information