• Averages can be shown in three different ways: using mean, mode and median.
• Ratios and proportions are helpful when comparing data sets where there is a relationship.
• When we look at how data has changed over time, we can calculate percentage increase and decrease.

Geographers use numbers - or data - all the time in every area of the subject. Some examples include using climate data when studying ecosystems, examining life expectancy when considering development or measuring river velocity during a geographical investigation. By studying this data, geographers are able to reach conclusions and interpret patterns and trends.

In geography, we collect and look at large amounts of raw data, so it's sometimes useful to use averages. During a data collection such as a pedestrian count, for example, a geographer might do three separate counts at the same location to ensure a good data set. An average of these data would then be used.

One way to calculate an average is by measuring central tendency - the average of a set of data. There are three ways of doing this.

Let's take, for example, the following dataset:

1, 4, 3, 3, 2, 5

The median is the middle figure in a data set. To work this out, the numbers are placed in numerical order and the central number or numbers identified. In the above example the median would be 3 as the numbers in order would be read 1, 2, 3, 3 4, 5.

The middle numbers here are both 3, meaning that the median is 3.

The mode is the most common value in a set of data. In the data set above, 3 appears twice whereas all the other numbers appear only once. Therefore, the mode in this dataset is 3.

Another useful statistic technique is calculating percentage increase or decrease, also known as percentage change. This technique helps us to compare sets of data and to look at how the data may have changed over time.

There are three steps involved in calculating percentage change:

Step 1 - calculate the difference between the two numbers
Step 2 - divide the difference by the original number
Step 3 - multiply the answer by 100 to convert to a percentage

The number of tourists to the UK decreased from 32.3 million in 2019 to 9.7 million in 2020. What is the decrease in visitor numbers, as a percentage?

Step 1 - calculate the difference between the two numbers

32.3 million - 9.7 million = 22.6 million

Step 2 - divide the difference by the original number

22.6 million ÷ 32.3 million = 0.70

Step 3 - multiply the answer by 100 to convert to a percentage

0.70 x 100 = 70%

Conclusion: There has been a 70% decrease in tourists between 2019 and 2020.

Ratios are used when there is a relationship between two types of data. Ratios are shown as two numbers separated by a colon, like this:

3 : 170

To work out the number of doctors per thousand people in a country, for example, the following steps should be taken:

Step 1 - divide the number of doctors by the number of people.
Step 2 - multiply this answer by 1000 as the ratio is not per person but per thousand.

1. Calculate the number of doctors per thousand people in Cuba.

Step 1- divide the number of doctors by the number of people

97, 000 ÷ 11, 300 000 = 0.00856

Step 2 - multiply this answer by 1000 as the ratio is not per person but per thousand

0.00856 x 1000 = 8.56 doctors per thousand people in Cuba or 8.56 : 1000

2. Calculate the number of doctors per thousand people in the UK.

Step 1- divide the number of doctors by the number of people

187, 419 ÷ 66, 650 000 = 0.002812

Step 2 - multiply this answer by 1000 as the ratio is not per person but per thousand

0.00856 x 1000 = 2.81 doctors per thousand people in the UK or 2.81 : 1000

A ratio is useful as we can compare these two countries even though they have different population sizes. Cuba has 8.56:1000 whereas the UK only has 2.81:1000.