Use mean when values share a unit and each contributes equally to a total.
Statistics guide
Mean, Median, Mode, and Range: When to Use Each
Mean is the arithmetic average (sum/n). Median is the middle value when sorted. Mode is the most frequent value. Range = max − min. For {30k, 34k, 35k, 38k, 200k}: mean = $67.4k (pulled up by outlier), median = $35k (representative of typical), mode = none, range = $170k. Reporting mean alone for skewed income data overstates the typical salary by 93%.
Short answer
Mean describes the arithmetic average. Median describes the middle ordered value — use it instead of mean when data is skewed. Mode describes the most frequent value — use it for categorical data. Range measures the distance from smallest to largest — it is a spread measure, not a center measure.
Same dataset, four different summaries
Switch examples to see which summary tells the clearest story and which can mislead.
Example input 72, 80, 80, 88, 96
Mean and median are close (gap = 3.2, or 4%). All four summaries are useful — data is not strongly skewed.
Mean = 83.2 | Median = 80 83.2 / 80
Mode = 80 | Range = 24 80 / 24
Side-by-side comparison
Use this table when you need a fast, practical distinction before choosing a calculator.
| Feature | Option A | Option B |
|---|---|---|
| Mean (AM) | Sum divided by count. Uses all values. | Best for additive numeric data without strong outliers. Wrong for categories. |
| Median | Middle value when sorted. Ignores magnitudes. | Best for skewed data: income, home prices, response times. Resistant to outliers. |
| Mode | Most frequent value. Can be multiple or none. | Best for categories and nominal data. Can apply to numeric data too. |
| Range | Max − min. Uses only two values. | Quick spread check. Not a center measure. Sensitive to extreme outliers. |
| Standard deviation | Typical distance from the mean. Uses all values. | Better spread summary than range, but requires numeric data and is sensitive to outliers. |
Which summary fits your question?
Start with what you want to describe, not with what is easiest to calculate.
Use median when a few extreme values would pull the mean away from the typical value.
Use mode for repeated values, categories, or to find the most common choice.
Use range for a quick check. Use standard deviation for a complete spread picture.
Examples that make the choice clear
Skewed data: median reports the typical income, mean does not
Incomes: $30k, $34k, $35k, $38k, $200k. Mean = ($30k+$34k+$35k+$38k+$200k)/5 = $67.4k. Median = $35k (third of five values when sorted). The $200k earner pulls the mean $32.4k above four out of five workers. Reporting mean = $67.4k implies a typical salary that no one in the group actually earns. Median = $35k correctly represents the person in the middle.
Categorical data: only mode is valid
Survey answers: A, B, B, C, B, A. Mode = B (appears 3 times). Mean and median are undefined for non-numeric categories. Do not calculate 'average survey answer' — report mode (most frequent) and frequency distribution instead.
Common mistakes
These are the errors most likely to make the correct formula return a misleading answer.
Reporting mean for skewed income or price data without context
For {$30k, $34k, $35k, $38k, $200k}: mean = $67.4k overstates typical by 93%. Always report median alongside mean for skewed distributions, or report both with a note explaining the outlier.
Calling range an average or center measure
Range = max − min. For {72,80,88,96}: range = 24, not the center. Range describes width. Use it alongside mean or median, not instead of them.
Calculating mean for categorical data
A, B, B, C, B, A cannot be averaged numerically. Mean requires numeric values. Use mode (= B) or frequency counts (A: 2, B: 3, C: 1) for categorical summaries.
Frequently asked questions
Which is better, mean or median?
Mean is better when values are additive, symmetric, and no extreme outliers exist. Median is better when data is skewed. For {$30k,$34k,$35k,$38k,$200k}: mean = $67.4k, median = $35k. The $200k value makes mean 93% above median — in that case, median is more representative. Report both when the gap is large.
Can a dataset have more than one mode?
Yes. {2, 4, 4, 6, 8, 8}: bimodal — modes are 4 and 8 (each appears twice). {1,2,3,4,5}: no mode — every value appears once. Mode is most useful when one value clearly dominates.
Is range enough to describe spread?
For a quick check, yes. Range = max − min tells you the width of the distribution using only two values. But range is blind to what happens in between. {1, 50, 50, 50, 99} and {1, 25, 50, 75, 99} both have range = 98, but the first dataset is much more clustered. Use standard deviation for a full spread picture.