Mean, Median, Mode, and Range

When scientists collect data, they need a few numbers that sum up the whole set. The four you will use most on the test are the mean, median, mode, and range. Each describes the data in a different way, and knowing which one a question wants is half the battle.

This lesson defines all four, shows how to find each, and points out when one is more useful than another.

Mean: The Average

The mean is what most people call the average. Add up all the values and divide by how many there are. For the data set \(4, 8, 6, 10, 2\): \[ \text{mean} = \dfrac{4+8+6+10+2}{5} = \dfrac{30}{5} = 6. \] The mean uses every value, which makes it powerful — but also sensitive to extreme values, as we will see.

Median: The Middle

The median is the middle value once the numbers are in order. Sort the set first: \(2, 4, 6, 8, 10\). The middle number is \(6\), so the median is \(6\). If there is an even number of values, the median is the mean of the two middle ones. The median is useful when a few very large or very small values would pull the mean in a misleading direction.

Mode and Range

The mode is the value that appears most often. In \(3, 7, 7, 2, 9\), the mode is \(7\). A set can have more than one mode, or none at all if nothing repeats. The range measures spread: subtract the smallest value from the largest. For \(2, 4, 6, 8, 10\), the range is \(10-2 = 8\). Range tells you how far apart the data is, not where its center is.

Here is when the choice matters. Suppose most salaries in a small company are near \(40{,}000\), but the owner earns \(400{,}000\). The mean is dragged upward by that one large value, so the median gives a fairer picture of a “typical” salary. Knowing this is often the point of a test question.

Watch: A Short Video Lesson

Math with Mr. J walks through this skill clearly in a few minutes. It is a helpful companion to the reading above:

A Routine for These Questions

1. Mean: add all values, divide by the count.
2. Median: sort the values, take the middle (or the average of the two middle).
3. Mode: find the most frequent value.
4. Range: largest minus smallest.

Practice

Use the data set \(5, 9, 9, 12, 5, 8\).

1. What is the mean?
2. What is the median?
3. What is the mode?
4. What is the range?
5. Which measure is most affected by one very large value?
6. When is the median a better “typical” value than the mean?

Answers

1. \(\dfrac{5+9+9+12+5+8}{6} = \dfrac{48}{6} = 8\).
2. Sorted: \(5,5,8,9,9,12\); middle two are \(8\) and \(9\), so median \(= 8.5\).
3. Both \(5\) and \(9\) appear twice, so the set has two modes: \(5\) and \(9\).
4. \(12-5 = 7\).
5. The mean.
6. When a few extreme values would distort the mean.

Where This Fits in Your Science Prep

These summary measures work hand in hand with reading data tables and trends and predictions. They also build on percentages. See all topics on the Science Topics Hub.