Calculating the Range

Welcome to Measuring Spread with Range and IQR, the third course in our statistics learning path! In the first two courses, you learned how to read distributions from graphs and how to summarize center using mode, median, and mean. Those skills gave you a way to describe where data tends to cluster. Now we move to the next natural question: how spread out is the data? This course focuses on tools that answer that question, and in this first lesson we start with the simplest one of all: the range.

Knowing the center of a dataset tells you a lot, but it never tells the whole story. Imagine two coffee shops that both sell an average of 200 cups per day. At Shop A, daily sales bounce between 190 and 210 cups. At Shop B, they swing from 50 cups on slow days to 350 on busy ones.

The average is the same, yet the day-to-day experience is completely different. That difference is what we call spread (also known as variability). Measuring spread helps us understand how consistent or unpredictable the data is, and it is an essential companion to any measure of center.

The range is the simplest way to measure spread. It answers one focused question: how far apart are the most extreme values in the dataset?

To compute it, subtract the smallest value (the minimum) from the largest value (the maximum):

The result tells you the total span the data covers. A larger range means the data stretches over a wider interval; a smaller range means the values stay closer together.

Suppose you recorded the daily high temperatures (in °F) for one week:

Here is the process:

1. Find the maximum. Scanning the values, the highest temperature is $72$.
2. Find the minimum. The lowest temperature is $58$.
3. Subtract. $\text{Range} = 72 - 58 = 14$ °F.

The range is 14 °F, meaning all seven daily highs fall within a 14-degree window. Notice that you do not need to sort the data first — you only need to locate the largest and smallest values.