How do I calculate the interquartile range?

To calculate the interquartile range, subtract the first quartile (Q1) from the third quartile (Q3).

The interquartile range (IQR) is a measure of statistical dispersion, which indicates the spread of the middle 50% of your data. To find the IQR, you first need to arrange your data in ascending order. Once your data is ordered, you can identify the quartiles. Quartiles divide your data into four equal parts. The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half.

For example, if you have the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, you would first find the median, which is the middle value. In this case, the median is 11 (the average of 10 and 12). The lower half of the data is 2, 4, 6, 8, 10, and the upper half is 12, 14, 16, 18, 20. The median of the lower half (Q1) is 6, and the median of the upper half (Q3) is 16.

To calculate the IQR, subtract Q1 from Q3: IQR = Q3 - Q1. In this example, IQR = 16 - 6 = 10. This means the middle 50% of your data is spread over a range of 10 units.

Understanding the IQR is useful in geography for analysing data sets such as rainfall, temperature, or population figures, as it helps to identify the variability and detect any outliers in the data.