Geometric Mean Calculator Statistics guide
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%.
Mean describes the arithmetic average. Median describes the middle ordered value — use it instead of mean when data is skewed, as the geometric mean vs median guide explains. 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, and standard deviation describes that spread far more precisely.
Switch examples to see which summary tells the clearest story and which can mislead.
Mean and median are close (gap = 3.2, or 4%). All four summaries are useful — data is not strongly skewed.
Check the input type and formula side by side before calculating.
| Method | Each describes 'typical' differently — they are not interchangeable | Range is not an average — it measures width |
|---|---|---|
| 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. |
Mean and median are both correct arithmetic on the same nine rows. They differ by $31,000, and only one of them describes anyone who actually works there.
Situation: Nine salaries at a startup: $38k, $42k, $45k, $47k, $47k, $55k, $58k, $62k, and a $310k founder.
| Step-by-step: how to use this calculator correctly | Mean | Median |
|---|---|---|
| 1. Prepare the data | Order does not matter; every value is used. | Sort first: 38, 42, 45, 47, 47, 55, 58, 62, 310. |
| 2. Combine | Sum all nine = $704,000 | Find the middle position: (9 + 1) / 2 = 5th value |
| 3. Compute | 704,000 / 9 = $78,222 | The 5th value = $47,000 |
| 4. Test against the team | Higher than 8 of the 9 actual salaries. | Four people earn less, four earn more — a genuine middle. |
| 5. Remove the founder | Falls to $49,250 — a $28,972 swing from one row. | Stays at $47,000 — completely unmoved. |
A single row moved the mean by nearly $29,000 and the median by nothing at all. When a distribution has a long tail — salaries, house prices, response times — the median is the honest headline, and the mean is the number that ends up in a misleading press release.
Each of the four measures has a boundary where it stops being informative. These are the ones that catch people out.
All-distinct data has no mode at all. The set {2, 4, 4, 6, 8, 8} has two of them. Mode is also the only one of the four that works on non-numeric data — the most common support category or shirt size — which is really what it is for.
Maximum minus minimum ignores everything in between, so {1, 50, 99} and {1, 2, 99} share a range of 98 despite completely different shapes. Use range as a quick bound, and standard deviation when the shape of the distribution actually matters.
For growth rates and ratios all four mislead, because each treats the values as additive. Annual returns of +50% and −50% give a mean of 0% and a median of 0%, yet the money is down 25%. That case needs geometric mean instead.
Start with what you want to describe, not with what is easiest to calculate.
Use mean when values share a unit and each contributes equally to a total.
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.
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.
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.
API latencies of 90, 95, 98, 102, 110, 115, and 4,000 ms produce a mean of 659 ms and a median of 102 ms. Not one request took 659 ms — the figure sits between the normal cluster and the single timeout, describing neither. This is why engineering teams report median and p95 rather than the average.
An order of S, M, M, L, M, XL has no meaningful mean or median, because the values are categories rather than quantities. Mode = M tells the warehouse what to stock. Range and standard deviation are undefined here, and any attempt to average the sizes numerically invents an ordering that does not exist.
A correct calculation can still mislead when the method or input type is wrong.
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.
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.
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.
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.
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.
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.
Median, whenever the distribution is skewed or you do not know its shape. It survives outliers and always corresponds to a real middle observation. Report the mean alongside it when the data is roughly symmetric — and report both when they disagree, because the size of the gap is itself information.
Average the two middle values after sorting. For eight sorted salaries, the median is the mean of the 4th and 5th. This is the one place where the median calculation borrows from the mean, and it is why a median can be a value that appears nowhere in the data.
No. Range is the distance between the two extremes and uses no other value in the set. Standard deviation measures the typical distance of every value from the mean. Two datasets can share an identical range while one clusters tightly in the middle and the other spreads evenly across it.