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Statistics Calculator

The default list of eight values (4, 8, 12, 16, 20, 14, 8, 11) has a mean of 11.625, a median of 11.5, a mode of 8, a range of 16, and a standard deviation of 4.742. Paste a list of numbers and get the summary statistics that describe it — mean, median, mode, range, and standard deviation, plus the count; values can be separated by commas, spaces, or both.

Mean
11.63
Median
11.50
Mode
8.00
Range
16.00
Std dev
4.742
Distribution
8 values · 8 bins
4
6
8
10
12
14
16
18
Inputs
Numbers (comma-separated)
This is the population standard deviation
It divides by n (8), giving 4.742. If these numbers are a sample of a larger group, divide by n−1 instead for 5.069.
Mean sits above the median
Mean 11.63 vs median 11.50: the gap signals skew — the mean is pulled toward the higher tail while the median holds the middle.
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Uses your inputs above
11.63 mean. Want to try a variation?
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The math

Reviewed 2026
Formula
mean = Σx/n; σ = √(Σ(x−μ)² / n)

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Example: how statistics is calculated

Step-by-step with default inputs

Suppose you put the default values into Statistics Calculator:

Numbers (comma-separated)
4, 8, 12, 16, 20, 14, 8, 11

Plug those into the formula mean = Σx/n; σ = √(Σ(x−μ)² / n) and the result is:

Mean
11.63

How to calculate statistics by hand

  1. Add all the values and divide by the count: 93 ÷ 8 = 11.625 is the mean.
  2. Sort the list and take the middle value; with 8 values, average the 4th and 5th: (11 + 12) ÷ 2 = 11.5 is the median.
  3. Count how often each value appears — 8 occurs twice, more than any other value, so the mode is 8.
  4. Subtract the minimum from the maximum for the range: 20 − 4 = 16.
  5. For the standard deviation, square each value's distance from the mean, average those squares, and take the square root.

How does the statistics calculator work?

The mean is the sum of the values divided by the count (93 ÷ 8 = 11.625 for the defaults). The median is the middle value after sorting — with an even count, the average of the two middle values. The mode is the most frequent value; if several values tie, the calculator reports one of them. Range is the maximum minus the minimum. Standard deviation uses the population formula, σ = √(Σ(x − μ)² / n), dividing by n rather than n − 1 — the right choice when your list is the entire dataset rather than a sample. If your numbers are a sample drawn from a larger population, the sample formula (dividing by n − 1) gives a slightly larger, less biased estimate: 5.069 instead of 4.742 for the default list.

Last reviewed July 2, 2026 · Editorial policy

Frequently asked questions

What's the difference between mean and median?

The mean is the arithmetic average; the median is the middle value once the list is sorted. The median resists outliers — add one huge value and the mean jumps while the median barely moves — which is why skewed data like incomes is usually summarized by the median.

Does this calculator use population or sample standard deviation?

Population — it divides the squared deviations by n, the full count. That is correct when your list is the whole dataset. If the list is a sample from something bigger, divide by n − 1 instead (Bessel's correction) for a less biased estimate.

What is the mode if no number repeats?

Strictly, a list where every value appears exactly once has no meaningful mode — every value ties at one occurrence. The calculator will still display one of the values, so check whether anything actually repeats before reading meaning into the mode.

What does standard deviation actually tell you?

How spread out the values are around the mean, in the same units as the data. A standard deviation of 4.742 on a mean of 11.625 means typical values sit roughly 5 units from the average; a smaller value means the data clusters more tightly.

How accurate is this statistics calculator?

The math is deterministic — the same inputs always produce the same output, and the formula is shown above. Accuracy of the answer for your situation depends on how well your inputs match reality and how well the formula models the question.

How do I share my result?

Hit Share at the top of the page. Every input you change is encoded in the URL, so a permalink reproduces exactly what you see. No account needed.