What's the difference between sample and population standard deviation?

Sample divides by N−1 (Bessel's correction); population divides by N. Use the sample form when your data is drawn from a larger group you couldn't measure entirely — the N−1 divisor corrects for the bias that the sample mean is closer to the sample data than the true mean would be. Use population when you measured everyone.

Why does the mode field sometimes show '—'?

When every value in your dataset appears exactly once, there is no mode by definition — no value is more frequent than the others. The calculator distinguishes that case from a bi- or multi-modal dataset (where multiple values tie for the highest frequency, and all are returned).

Which percentile method do you use?

Linear interpolation between the two closest ranks — the NIST default and the same convention NumPy's `linear` mode and most R defaults follow. It's continuous and gives sensible results on small datasets.

Does the calculator handle large datasets?

Up to several million values comfortably — the math is O(n log n) bounded by the sort. Browser memory becomes the limit before performance does.

Does the calculator store my data?

No. Every computation runs in your browser; nothing is sent to a server.

Statistics Calculator

One textarea, twelve statistics. Sample / population toggle, IQR included.

Paste any dataset — comma-, space-, or newline-separated — and the calculator returns the full descriptive-statistics summary: central tendency (mean, median, mode), spread (standard deviation, variance, range, IQR), and the quartile cuts. The toggle at the bottom of the input switches between sample (n−1) and population (n) divisors for variance.

Dataset (comma, space, or newline separated)

8 values parsedUse population formula (divide by N instead of N−1)

Mean

5.0000

Median

4.5000

Mode

4.0000

Std deviation

2.1381

Variance

4.5714

Sum

40.0000

Min

2.0000

Max

9.0000

Range

7.0000

Q1 (25th)

4.0000

Q3 (75th)

5.5000

IQR

1.5000

Default formulas use Bessel’s correction (sample) for variance and standard deviation. Switch to the population form if your data is the entire population, not a sample drawn from one.

How to use

Paste your data
Any common delimiter works — commas, semicolons, spaces, tabs, newlines. Non-numeric tokens are silently dropped.
Pick sample or population
Sample (default) uses Bessel's correction (divide by N−1). Switch to population only if your data covers everyone in the group, not a sample drawn from one.
Read the result grid
12 statistics shown in three rows. Mean / median / mode in the highlighted top row; spread + quartile cuts below.

Worked example

Input: 2, 4, 4, 4, 5, 5, 7, 9

Statistic	Value
Mean	5
Median	4.5
Mode	4
Sample std dev	~2.14
Sample variance	~4.57
Min / Max / Range	2 / 9 / 7
Q1 / Q3 / IQR	4 / 5.5 / 1.5

Frequently asked questions

What's the difference between sample and population standard deviation?: Sample divides by N−1 (Bessel's correction); population divides by N. Use the sample form when your data is drawn from a larger group you couldn't measure entirely — the N−1 divisor corrects for the bias that the sample mean is closer to the sample data than the true mean would be. Use population when you measured everyone.
Why does the mode field sometimes show '—'?: When every value in your dataset appears exactly once, there is no mode by definition — no value is more frequent than the others. The calculator distinguishes that case from a bi- or multi-modal dataset (where multiple values tie for the highest frequency, and all are returned).
Which percentile method do you use?: Linear interpolation between the two closest ranks — the NIST default and the same convention NumPy's `linear` mode and most R defaults follow. It's continuous and gives sensible results on small datasets.
Does the calculator handle large datasets?: Up to several million values comfortably — the math is O(n log n) bounded by the sort. Browser memory becomes the limit before performance does.
Does the calculator store my data?: No. Every computation runs in your browser; nothing is sent to a server.

About

Why these statistics

The summary covers central tendency (mean, median, mode), spread (variance, SD, range), and shape (quartile cuts). For most real datasets these together answer the questions you actually have. Skewness and kurtosis aren't included; they're more useful as diagnostics for whether to assume normality, which is a question better answered by a histogram.

When to use sample vs population

If your dataset is a complete enumeration — every employee in your company, every transaction in March — use population. If it's a sample you'll generalise from — survey respondents, lab measurements — use sample (the default). At large N the difference is negligible; at small N it matters meaningfully.