Range definition
Range is a measure of spread in a set of data. It shows the difference between the largest value and the smallest value. To find the range, subtract the smallest value from the largest value. For example, in the data set 4, 6, 9, 11 and 15, the largest value is 15 and the smallest value is 4. The range is 15 minus 4, which equals 11.
The range tells us how spread out the data is from the lowest value to the highest value. A small range means the values are close together. A large range means the values are more spread out. For example, test scores of 48, 50, 51 and 52 have a small range, while scores of 12, 45, 80 and 95 have a much larger range. This helps compare consistency between data sets.
Range is used in statistics, data handling, science, geography, sport, finance, weather data and real-life comparisons. At GCSE level, students calculate the range from lists, tables and charts, then compare it with averages such as mean, median and mode. The range is often used to describe variation, reliability, consistency or spread in a data set.
The formula is range equals highest value minus lowest value. For example, if daily temperatures in a week are 8, 10, 12, 15, 16, 18 and 20 degrees, the range is 20 minus 8, which equals 12 degrees. This means the temperatures varied by 12 degrees across the week. The units of the range are the same as the units of the original data.
The range is easy to calculate, but it can be affected strongly by outliers. An outlier is a value that is much bigger or smaller than the rest of the data. For example, the data set 5, 6, 7, 8 and 100 has a range of 95 because of the outlier 100. Most values are close together, but the range becomes very large. This is why the range should be interpreted carefully.
Range is often used with averages. The mean, median and mode describe typical values, while the range describes spread. Two classes might have the same mean score but different ranges. One class may have scores close together, while another has scores that vary widely. This helps teachers, scientists and analysts understand not just the centre of the data but also how consistent the data is.
In grouped data, the exact range may not always be known because individual values are hidden inside class intervals. Students may estimate the range using the lowest possible value and highest possible value from the groups, or they may use other measures such as the interquartile range. The interquartile range focuses on the middle half of the data and is less affected by extreme values.
Related ideas include mean, median, mode, averages, spread, outliers, interquartile range, box plots, frequency tables and data interpretation. A clear definition of range helps students understand that statistics is about both typical values and variation. In exams, always identify the largest and smallest values correctly, subtract in the correct order and keep the correct units in the answer.