What's the difference between mean and median?

The mean is the average of all values, while the median is the middle value when data is ordered. The median is not affected by outliers, making it more reliable for data with extreme values.

Do I always have to order the data to find the median?

Yes, absolutely. The median is defined as the middle value of ordered data. Without ordering, you cannot identify which value is actually in the middle position.

Can the median be a value that is not in my data set?

For odd-sized data, the median is always one of your actual values. For even-sized data, the median is the average of two middle values, which may fall between them—for example, the median of 2 and 4 is 3, even if 3 is not in your original data.

When should I use median instead of mean?

Use the median when your data has outliers or extreme values, or when you want a typical value that cannot be skewed by very large or very small numbers. The median is especially useful for real-world data like house prices or salaries, where a few extremely high or low values would make the mean misleading.

Median

The median is the middle value of ordered data, most useful when your data contains outliers that would skew the mean value.

\tilde{x} = \text{middle value of the ordered data}

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What each symbol means

What Median takes

Symbol	Meaning
$\tilde{x}$	The symbol $\tilde{x}$ (x-tilde) denotes the median of a data set. If confused with $\bar{x}$ (which is the mean), you will calculate the wrong center measure.

When to use it

Use the median when you want to find a typical value and your data has outliers or extreme values that would make the mean misleading.

Level

Usually taught in: Pre-Algebra · Appears on: SAT, ACT

Worked examples

1. Find the median of five test scores

Problem

Find the median of 3, 7, 2, 9, 5

$3, 7, 2, 9, 5$
Write down the given data.
$2, 3, 5, 7, 9$
Arrange the values from smallest to largest.
$n = 5$
Count the number of values; there are 5 data points (an odd number).
$\text{Position} = \frac{n+1}{2} = \frac{5+1}{2} = \frac{6}{2} = 3$
For an odd number of values, the median is at position $\frac{n+1}{2} = 3$ .
$\tilde{x} = 5$
The value at position 3 of the ordered data is 5.

Answer: $\tilde{x} = 5$

With an odd number of data points, the median is exactly the middle value. We ordered the data and identified the value at the center position.

2. Find the median of six values including negatives

Problem

Find the median of

-2, 5, 3, -1, 8, 2

$-2, 5, 3, -1, 8, 2$
Write down the given values.
$-2, -1, 2, 3, 5, 8$
Arrange from smallest to largest, treating negative numbers correctly.
$n = 6$
We have 6 values, which is an even number.
$\text{Middle positions} = 3 \text{ and } 4$
For even $n$ , there is no single middle value. The two middle positions are $\frac{n}{2} = 3$ and $\frac{n}{2} + 1 = 4$ .
$\text{Values at positions 3 and 4:} \; 2 \text{ and } 3$
From the ordered data, the 3rd value is 2 and the 4th value is 3.
$\tilde{x} = \frac{2 + 3}{2} = \frac{5}{2} = 2.5$
The median for even-sized data is the average of the two middle values.

Answer: $\tilde{x} = 2.5$

With an even number of data points, there is no single middle value, so we average the two middle values to find the median.

3. Find the median points in a basketball season

Problem

A player scored the following points over 7 games in her basketball season: 12, 18, 15, 22, 14, 19, and 16 points. Find the median points per game.

$12, 18, 15, 22, 14, 19, 16$
Write down the point totals from all 7 games.
$12, 14, 15, 16, 18, 19, 22$
Arrange the game scores from smallest to largest.
$n = 7$
Count the games; there are 7 data points (an odd number).
$\text{Position} = \frac{n+1}{2} = \frac{7+1}{2} = \frac{8}{2} = 4$
The median is at position $\frac{n+1}{2} = 4$ .
$\tilde{x} = 16$
The value at position 4 in the ordered data is 16 points.

Answer: $\tilde{x} = 16 \text{ points}$

The median of 16 points tells the player that she scored more than this in half her games and less than this in the other half. This is a useful summary of typical performance that is not skewed by the one very high game of 22 points.

Common mistakes

Where Median usually goes wrong

The mistake	Why it is wrong	The fix
The median of 3, 7, 2, 9, 5 is 3	3 is the position number, not the value at that position.	Order the data to get 2, 3, 5, 7, 9. Then identify position $\frac{n+1}{2} = 3$ and read the value at that position: 5.
The median of 2, 4, 6, 8 is 4	With 4 values (even), the median must be the average of the two middle values (4 and 6), not just the first of the two.	Calculate $\frac{4+6}{2} = \frac{10}{2} = 5$ ; the median is 5.
The median of 8, 2, 5, 1, 9 is 5	Without ordering the data first, the position of the middle value cannot be identified correctly.	Always order first: 1, 2, 5, 8, 9. Then find position $\frac{5+1}{2} = 3$ , so the median is the value at position 3, which is 5.

Tips and when to use something else

Use the median instead of the mean when your data contains outliers or extreme values that could skew the average.
The median always requires ordering the data first; skipping this step will give you the wrong answer.
For odd-sized data, the median is always one of your actual data values; for even-sized data, it may fall between two values.
Do not confuse the median with the mode (most frequent value) or the mean (average of all values)—each measures center differently.

Related formulas

Arithmetic MeanArithmetic Mean is the average value found by adding all numbers in a dataset and dividing by how many numbers there are.ModeMode is the value that appears most frequently in a dataset; use it to identify the most common outcome when comparing preferences or observations.Range of a Data SetRange measures the spread of a data set by finding the difference between the maximum and minimum values, telling you how dispersed your data is.Interquartile RangeThe interquartile range measures the spread of the middle 50% of your data, telling you how compressed or spread out typical values are.Outlier RuleThe Outlier Rule identifies data values farther than 1.5 times the interquartile range from the quartiles—use it to flag unusual observations.

Frequently asked questions

What's the difference between mean and median?: The mean is the average of all values, while the median is the middle value when data is ordered. The median is not affected by outliers, making it more reliable for data with extreme values.
Do I always have to order the data to find the median?: Yes, absolutely. The median is defined as the middle value of ordered data. Without ordering, you cannot identify which value is actually in the middle position.
Can the median be a value that is not in my data set?: For odd-sized data, the median is always one of your actual values. For even-sized data, the median is the average of two middle values, which may fall between them—for example, the median of 2 and 4 is 3, even if 3 is not in your original data.
When should I use median instead of mean?: Use the median when your data has outliers or extreme values, or when you want a typical value that cannot be skewed by very large or very small numbers. The median is especially useful for real-world data like house prices or salaries, where a few extremely high or low values would make the mean misleading.

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Reviewed 2026-09-18