When we talk about the average of a group of numbers in statistics, we often mention three terms: mean, median, and mode. These terms help us understand a collection of data by summarizing it with one number.

While the mean (which is the average) is common, there are times when the median is a better choice.

So, when should you use the median instead of the mean? Let’s find out together!

What Are Mean and Median?

Before we get into when to use the median, let’s look at what mean and median mean.

• Mean: To find the mean, you add all the numbers together and then divide by how many numbers there are. For example, if we have the numbers 2, 4, 6, and 8, we find the mean like this:

$$\text{Mean} = \frac{2 + 4 + 6 + 8}{4} = \frac{20}{4} = 5$$

• Median: The median is the middle number when all the numbers are lined up in order. Using the same numbers (2, 4, 6, 8), they are already arranged. Since there are four numbers (an even amount), we take the two middle numbers and find their average:

$$\text{Median} = \frac{4 + 6}{2} = \frac{10}{2} = 5$$

Now that we know how to find both, let’s look at when the median is the better option.

When Should You Use the Median?

1. Outliers: Outliers are numbers that are much higher or lower than the others in the group. For example, consider these test scores: 55, 58, 60, 62, 70, and 100.

If we find the mean:

$$\text{Mean} = \frac{55 + 58 + 60 + 62 + 70 + 100}{6} = \frac{405}{6} \approx 67.5$$

This mean of about 67.5 doesn’t really show what most students scored, since 100 is much higher than the other scores.

Now, let’s find the median:

If we line up the test scores: 55, 58, 60, 62, 70, 100. The median would be:

$$\text{Median} = \frac{60 + 62}{2} = 61$$

In this case, the median (61) gives us a better understanding of the test scores.

2. Skewed Data: When the data is uneven or lopsided, the mean can be affected by extreme values. For example, look at this group of ages: 10, 12, 12, 12, 14, 14, 15, 17, 19, 70.

The mean age would be much higher because of the outlier (70):

$$\text{Mean} = \frac{10 + 12 + 12 + 12 + 14 + 14 + 15 + 17 + 19 + 70}{10} \approx 19.4$$

Here, the median would not be influenced by that high number:

If we arrange the ages: 10, 12, 12, 12, 14, 14, 15, 17, 19, 70, the median—found by taking the average of the two middle values—is:

$$\text{Median} = \frac{14 + 14}{2} = 14$$

3. Ranked Data: When you deal with ranked data, where the differences between the numbers aren’t clear, the median is very useful. For example, if you have rankings of 1st, 2nd, 2nd, and 4th in a competition, the median ranking (the middle value) is meaningful and makes more sense than calculating an average ranking.

Conclusion

In short, the median is often better than the mean when dealing with outliers, uneven distributions, or ranked data. It helps us see the big picture by reducing the impact of extreme values.

Understanding when to use these different measures is important in statistics, so you can understand and share your data accurately!