Title: Ranges, Quartiles and Percentiles
Course: UGQuants (SSPS) > Section: Univariate Analysis

Ranges, Quartiles and Percentiles

These measures offer a means of giving further detail, both numerically and visually, about continuous variables. They are also important in that they can help inform our decisions about how we might choose to restructure such variables, e.g. through recoding.

Range

The range simply represents the difference between the highest and lowest values taken by cases for a particular (ratio or interval) variable. So for example in the UK dataset of the 2010 European Social Survey, where the lowest value for age is 15 and the highest value 98, the range (in years) is 83. Note that in the language of statistics the range is not 15-98, as we would sometimes express it in everyday language. These values are in fact the minimum and maximum values respectively.

Quartiles and Percentiles

Essentially, quartiles are a means of dividing our data into four equally sized groups (i.e. 4 groups with an equal or nearly equal number of cases within them). You might also sometimes encounter quintiles or deciles, which divide data into five and ten equally sized groups respectively. These groups are based on values for each case in ascending order.

So the first (or ‘lower’) quartile is the value below which lie (approximately) the quarter of our cases with the lowest values. The third (or ‘upper’) quartile is the value above which lie (approximately) the quarter of our cases with the highest values. The second quartile is the same as the measure of central tendency known as the median. A related measure is the interquartile range, which effectively ignores the cases in the lowest and highest quartiles and calculates the difference between the lowest and highest values for the 50% of cases that lie closest to the middle of the distribution, i.e. closest to the median. So for example in the 2012 Scottish Social Attitudes Survey the interquartile range for age in years was 29 (the difference between the value for the first quartile – 33 – and the value for the third quartile – 62.

The first, second and third quartiles are also known respectively as the 25th, 50th and 75th percentiles. Percentiles divide our cases into 100 (approximately) equal groups, and so we can choose to calculate the values below and above which any proportion of our cases – from 1/100 to 99/100 – lie. So for example the value for the 1st percentile would be the value below which the 1% of cases with the lowest values lie; the 90th percentile would indicate the value above which the 10% of cases with the highest value lie, etc.

You might be familiar with the concept of percentiles as a means to place students’ grades within a class hierarchy, but in terms of social and political research they can be very useful in conveying information about, e.g. relative poverty (or wealth), health, educational attainment, etc. For example: