Mean, Median, and Mode: When to Use Each (With Examples)

Quick Answer

Mean.
Add all values and divide by the count. Use it when your data is roughly symmetric and free of extreme outliers. It's the most common measure in research.

Median.
The middle value when your data is sorted. Use it when you have outliers or skewed data. It's the right choice for income, home prices, and reaction times.

Mode.
The most frequent value. Use it for categorical data (favorite color, political party) or to describe the most common response in a survey.

The decision rule.
Continuous and symmetric data: mean. Continuous and skewed: median. Categorical data: mode.


What These Three Statistics Measure

Mean, median, and mode are the three main measures of central tendency. Each one tries to describe the "typical" value in a dataset. They give different answers because they use different definitions of "typical."


The mean uses every value in the calculation. The median ignores everything except the middle. The mode counts only how often each value appears. Same data, three different answers. Picking the right one depends on what your data looks like and what you're trying to communicate.


The Mean

The mean is what most people call "the average." Add up all the values and divide by the number of values. That's it.


Formula

The formula for the sample mean is:


M = (Σ x) / n

Where Σ x is the sum of all values and n is the number of values.


In APA format, you report the mean as italicized M. The population mean uses the Greek letter μ (mu). Most research uses sample data, so M is what you'll see most often.


Worked example

A researcher measures the test scores of 10 students:

72, 78, 81, 85, 85, 87, 88, 90, 92, 94


Add them up: 72 + 78 + 81 + 85 + 85 + 87 + 88 + 90 + 92 + 94 = 852.

Divide by 10: 852 / 10 = 85.2.

The mean is M = 85.2.


When the mean works well

The mean works when your data is roughly symmetric and doesn't contain extreme outliers. Test scores, height, IQ, reaction times that fall in a normal range. These all distribute symmetrically around a central value, and the mean accurately represents that center.


When the mean fails

The mean breaks when data is skewed or contains outliers. The classic example is income. Most people earn modest amounts. A few earn enormous amounts. The handful of extreme high earners pulls the mean upward, so the average no longer describes the typical person.


Consider this small dataset of yearly incomes:

$32,000, $38,000, $41,000, $45,000, $48,000, $52,000, $58,000, $61,000, $67,000, $980,000


The mean is $142,200. But nine out of ten people in this group earn less than $70,000. The mean misrepresents the typical income. The one billionaire-adjacent outlier distorts everything.


The Median

The median is the middle value when your data is sorted from smallest to largest. Half the values fall below it. Half fall above it.


How to find it

First, sort your data in order. Then find the middle.

  • If you have an odd number of values, the median is the middle one.
  • If you have an even number of values, the median is the average of the two middle values.

Worked example with odd n

A researcher measures reaction times (in milliseconds) for 7 participants:

280, 295, 310, 325, 340, 380, 520


Already sorted. The middle value (the 4th of 7) is 325. The median is 325 ms.

Note the outlier at 520. The mean of this same data is 350, pulled upward by the slow responder. The median is unaffected. For reaction time data, the median is almost always the better choice.


Worked example with even n

A researcher measures the same reaction times for 8 participants:

280, 295, 310, 325, 340, 380, 420, 520


The two middle values are the 4th and 5th: 325 and 340. Average them: (325 + 340) / 2 = 332.5. The median is 332.5 ms.


When the median works well

Use the median when your data is skewed or has outliers. The classic cases are income, home prices, reaction times, and any variable where extreme values are common. The median is also the right choice for ordinal data, where the gaps between values aren't meaningful (a Likert scale where 4 is one step above 3 but the "size" of that step isn't a real quantity).


When the median is less useful

The median ignores most of your data. For small datasets that are roughly symmetric, this means throwing away information that the mean uses. If your data has no outliers and isn't skewed, the mean usually gives a better summary.


The Mode

The mode is the most frequent value in your dataset. It's the only measure of central tendency that works for categorical data.


How to find it

Count how many times each value appears. The value that appears most often is the mode.


Worked example with categorical data

A survey asks 100 students what their preferred study time is:

  • Morning: 18 students
  • Afternoon: 24 students
  • Evening: 41 students
  • Late night: 17 students

The mode is "Evening." That's the most common response. The mean and median don't apply here because the categories don't have numerical values you can add or sort.


Worked example with continuous data

Test scores from 12 students:

72, 78, 81, 85, 85, 85, 88, 90, 92, 94, 96, 98


The value 85 appears three times. Every other value appears once. The mode is 85.


Bimodal and multimodal data

Some datasets have two or more values that tie for most frequent. A dataset with two modes is bimodal. A bimodal distribution often suggests two distinct groups within your sample (a class with both highly prepared and underprepared students, for example). When you see bimodality, investigate before treating the data as one group.


When the mode works well

The mode is essential for categorical data. Favorite color, political party, type of degree, blood type. For continuous data, the mode is less commonly reported but useful when you want to describe the most typical response in a survey.


Same Data, Three Different Answers

A clear example shows why picking the right measure matters. Consider this dataset of monthly income for 11 people (in thousands of dollars):

2.5, 3.0, 3.2, 3.5, 3.5, 3.8, 4.0, 4.2, 4.5, 5.0, 47.0


  • Mean: Sum is 84.2. Divided by 11: M = $7,655 per month.
  • Median: Middle value (the 6th of 11): $3,800 per month.
  • Mode: The value 3.5 appears twice. Mode = $3,500 per month.

Same data. Three answers ranging from $3,500 to $7,655. The mean is wildly higher than the typical person earns because one high earner skews it. The median accurately reflects the middle of the distribution. The mode tells you the most common income point. If you reported only the mean here, readers would wrongly conclude that the average person in this group earns nearly $8,000 a month. They don't.


How to Decide Which to Use

Pick your measure based on what kind of data you have.

  • Categorical or nominal data (favorite color, type of treatment, country of origin). Use the mode. Mean and median don't apply.
  • Ordinal data (Likert scales, ranks). Use the median. Some researchers report means on Likert scales, but the median is more defensible because the gaps between scale points aren't equal.
  • Continuous data, symmetric distribution (height, test scores, IQ). Use the mean. It uses all the data and is the standard reporting choice.
  • Continuous data, skewed distribution or outliers (income, home prices, reaction times). Use the median. It's robust to extreme values.

When in doubt, report both the mean and the median. If they're close, your data is symmetric and either works. If they differ substantially, you have skew or outliers, and the median is the better summary.


Reporting in APA Format

APA 7 has specific conventions for reporting these statistics.


Mean. Italicized M, followed by an equals sign and the value. Always pair the mean with a standard deviation when describing a sample. Example:

Participants scored above the population average (M = 85.2, SD = 7.3).


Median. Capitalize and italicize Mdn. Example:

Reaction times were faster in the experimental condition (Mdn = 325 ms) than the control condition (Mdn = 410 ms).


Mode. Capitalize Mode in full (not italicized as a single letter). Example:

The most common preferred study time was evening (Mode = evening, 41% of respondents).


Common Mistakes

  • Reporting the mean for skewed data. The classic income example. The mean misrepresents the typical value when extreme outliers are present.
  • Using the mean on a Likert scale without justification. Some fields accept this. Others require the median. Check your discipline's conventions.
  • Reporting only the mean without the standard deviation. APA requires both. A mean alone tells readers the center but not the spread.
  • Forgetting to check for bimodality. A bimodal distribution often indicates two distinct subgroups in your sample. Report the mode and investigate before averaging.
  • Confusing "no mode" with "mode of zero." If every value appears exactly once, there's no mode. Don't write "Mode = 0." Write "No mode" or report the most frequent grouping.

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Frequently Asked Questions

When should I use the mean vs. the median?

Use the mean when your data is continuous and roughly symmetric, without extreme outliers. The mean uses every value in the calculation and is the standard reporting choice in most research. Use the median when your data is skewed or contains outliers, or when you have ordinal data like Likert scales. The median is the middle value and isn't affected by extreme scores. If you're unsure, report both. If they're close, your data is symmetric. If they differ, the median is the more defensible summary.


Can I use the mean with a Likert scale?

Conventions vary by field. Strict measurement theorists argue that Likert scales are ordinal data, so only the median is appropriate. The gap between "agree" and "strongly agree" isn't necessarily the same as the gap between "neutral" and "agree." Many applied fields routinely use the mean anyway, treating Likert items as approximately continuous when scales have five or more points and responses cluster around the middle. Check what your discipline does. When in doubt, report both the mean and the median.


What does it mean if my data is bimodal?

Bimodal data has two distinct peaks rather than one. It often signals that your sample contains two different subgroups mixed together. For example, exam scores in a class with both well-prepared and underprepared students might be bimodal. When you see bimodality, investigate before averaging. The mean of a bimodal distribution often falls between the two peaks and doesn't represent any actual subgroup. Split your data by the relevant variable, if you can identify it, and analyze the subgroups separately.


Why is the median better for income data?

Income distributions are heavily right-skewed. Most people earn modest amounts. A small number of people earn enormous amounts. The high earners pull the mean upward, often well above what most people in the group actually make. The median, as the middle value, isn't affected by the extreme high earners. It accurately tells you what the person in the middle of the distribution earns. This is why government statistics agencies report median household income, not mean household income.


What is the formula for the mean?

The formula for the sample mean is M = (Σ x) / n, where Σ x is the sum of all values and n is the number of values. The population mean uses the Greek letter μ (mu) instead of M. In research papers reporting sample data, you'll see M most often. The formula is the same in both cases: add up all the values and divide by how many there are.


Do I need to report all three?

No. In most papers, you report whichever measure best describes your data. For continuous symmetric data, that's the mean. For skewed data, that's the median. For categorical data, that's the mode. Reporting all three is unnecessary and clutters your results. The exception is when your data is borderline and you want to show readers that the choice doesn't change your conclusions. In that case, reporting mean and median together demonstrates robustness.

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