Mean, Median, Mode, and Range: A Plain-English Statistics Guide for 2026

Mean, median, mode, and range are the first four statistics every student learns. They appear on the 6th-grade state test, the SAT, and every introductory stats unit through college. Most students can recite the definitions but choose the wrong measure for the question on test day.

This guide walks through each one, explains when to use which, and ends with the outlier trick that separates a B from an A in statistics.

The Four Definitions

• Mean: the average. Add all values and divide by the count.
• Median: the middle value when the data is in order.
• Mode: the value that appears most often.
• Range: the difference between the largest and smallest values.

Mean, median, and mode are all measures of center. Range is a measure of spread. The distinction matters for the SAT.

Mean: Step by Step

For the data 4, 7, 10, 12, 17:

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1. Add: 4 + 7 + 10 + 12 + 17 = 50.
2. Count: 5 values.
3. Divide: 50 / 5 = 10.

Mean = 10.

The mean is also called the average in everyday language and expected value in probability. All three words refer to the same number.

Median: Step by Step

For 4, 7, 10, 12, 17:

1. Sort: already sorted.
2. Find the middle. 5 values → middle is the 3rd → 10.

Median = 10.

When there is an even number of values:

For 4, 7, 10, 12, 17, 20:

1. Sort.
2. The middle two are 10 and 12. Average them: (10 + 12)/2 = 11.

Median = 11.

The median is the value at position (n+1)/2 in the sorted list (or the average of the two middle values if n is even).

Mode: Step by Step

For 3, 5, 5, 7, 8, 8, 8, 10:

The most frequent value is 8 (appears three times).

Mode = 8.

A data set can have:
– One mode (unimodal).
– Two modes (bimodal).
– No mode (every value appears the same number of times).

Range: Step by Step

For 4, 7, 10, 12, 17:

Largest − smallest = 17 − 4 = 13.

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Range = 13.

Range measures spread, not center. A large range means the data is spread out; a small range means it is tightly clustered.

When to Use Which

• Mean when the data has no big outliers and you want a balanced measure.
• Median when there are outliers (or when the data is skewed). Median is not influenced by extreme values.
• Mode when you need the most common value (like the most-purchased size of shoe, or the most-frequent answer on a quiz).
• Range to measure spread.

Five houses on a street are worth $200K, $210K, $220K, $230K, and $5M.
Mean: $1,172,000. Misleading — only one house costs that.
Median: $220K. Much more representative.

This is exactly why the news always reports median home price, not mean.

Outliers: The Most Tested Concept

An outlier is a value far from the rest. A common rule of thumb: any value more than 1.5 × IQR (interquartile range) below the first quartile or above the third quartile is an outlier.

The casual definition you will use on most tests: a value clearly far from the rest.

Mean is sensitive to outliers; median and mode are not.

That single fact answers more SAT statistics questions than any other.

Data: 3, 4, 5, 6, 7. Mean = 5. Median = 5.
Change to: 3, 4, 5, 6, 100. Mean = 23.6. Median = 5.

The median did not budge. The mean spiked.

Weighted Mean

Sometimes values have different weights. The weighted mean accounts for that.

A student’s grade is 30% homework, 30% quizzes, 40% final.
Scores: homework 88, quizzes 90, final 75.

Weighted mean = 0.30 · 88 + 0.30 · 90 + 0.40 · 75 = 26.4 + 27 + 30 = 83.4.

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Notice this is not the simple mean (88 + 90 + 75) / 3 = 84.33. The final pulled it down because it has more weight.

Quick Worked Examples

Data: 12, 15, 18, 22, 23, 23, 27.
Mean = (12 + 15 + 18 + 22 + 23 + 23 + 27) / 7 = 140 / 7 = 20.
Median = 22 (middle of 7 values).
Mode = 23.
Range = 27 − 12 = 15.

Data: 10, 10, 10, 10.
Mean = 10. Median = 10. Mode = 10. Range = 0.
When all values are equal, every measure of center is the same and the range is 0.

Data: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Mean = 5. Median = 5. Mode = none (or all values, depending on textbook). Range = 8.

Comparing Distributions

The SAT loves these. You see two histograms side by side and have to compare measures.

• Mean is pulled by long tails. A right-skewed graph (long tail on the right) has mean > median.
• Median sits in the middle of the count.
• Symmetric distributions have mean ≈ median.
• Spread (range, IQR, standard deviation) describes how wide the distribution is.

“Which has a larger mean: a left-skewed distribution or a right-skewed distribution with the same median?”

The right-skewed one. Its right tail pulls the mean up.

Common Mistakes

1. Forgetting to sort before finding the median. Always order the data first.
2. Dividing by the wrong count for the mean. Count carefully; off-by-one is common.
3. Treating mode as a measure of center. Mode is most useful with categorical data; for numeric data the median or mean is usually more meaningful.
4. Confusing range with interquartile range (IQR). Range uses max minus min; IQR uses Q3 minus Q1.
5. Treating median as affected by outliers. It is not. That is the entire point of median.

A Quick Cheat Sheet

Frequently Asked Questions

Can a data set have no mean?
No. Every numeric data set has a mean (assuming at least one value).

Can a data set have more than one mode?
Yes. It can be bimodal (two modes) or have more.

Why is the median used for income reports?
Because incomes are right-skewed (a few very high incomes pull the mean up). The median better reflects what a typical person makes.

Is range the same as standard deviation?
No. Range is just max minus min. Standard deviation is the typical distance from the mean and uses every value.

Are mean and average the same thing?
Yes, in everyday usage and on most tests. In statistics, “mean” is more precise.

Closing Thought

Mean, median, mode, and range are the foundation of every stats course you will ever take. Drill the four definitions, remember that the mean is the one sensitive to outliers, and practice picking the right measure for the question.

For more practice, browse our Statistics worksheets and our full Math Topics library. When you are ready for a structured workbook, our Statistics collection covers measures of center and spread in depth.

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