Doing Math to Find Patterns

By the end of this lesson, you will be able to use simple calculations to describe relationships hidden inside a set of numbers.

Scientists rarely stop at collecting numbers. They do math on those numbers so the numbers can tell a story. When you work with quantitative data, which is information recorded as measurements or counts instead of words, calculations like averages, differences, ratios, and rates turn a messy list into a clear pattern you can argue about with evidence.

Picture a family drive from Dallas to Houston. The car's trip meter shows 240 miles, and the clock shows the drive took 4 hours. Dividing 240 by 4 gives 60, so the car averaged 60 miles per hour. That answer is a rate, which is a comparison of two different measurements, such as miles compared to hours. The rate tells you something the raw numbers did not: how fast the trip went on average. If a second trip covered 180 miles in 3 hours, that rate is also 60 miles per hour, so you can say both trips moved at the same average speed even though the distances were different.

You can also compare numbers by subtracting or by finding a percent. If one rain gauge in Lubbock collects 2 centimeters of rain and another in Beaumont collects 8 centimeters, the difference is 6 centimeters, and the ratio tells you Beaumont got four times as much. Calculating the mean, which is the sum of all values divided by how many values there are, helps you describe a whole set of measurements with one fair number.

Always keep your units attached, label what you calculated, and ask whether the answer makes sense. A number without meaning is not evidence yet.

Try it: if a school bus travels 90 miles in 3 hours, what is its average speed in miles per hour?