Statistics Calculator (mean, median, std dev, quartiles)
Paste a list of numbers (comma, space, or newline separated). The calculator returns descriptive statistics including central tendency, dispersion, and quartiles in one view.
- Count (n)
- 9
- Sum
- 222
- Mean (average)
- 24.6667
- Median
- 25
- Mode
- 25
- Range
- 28
- Minimum
- 12
- Maximum
- 40
- Q1 (25th percentile)
- 16.5
- Q3 (75th percentile)
- 32.5
- Standard deviation
- 9.1924
- Variance
- 84.5
How it works
What each statistic measures
Mean (average): sum divided by count. Sensitive to outliers — a single huge value can pull the mean far from the typical value. Best when data is roughly symmetric.
Median: the middle value when sorted. Robust to outliers — a few extreme values don't move it. Better than mean for skewed data like income or house prices.
Mode: the most frequent value. Most useful for discrete data (survey responses, dice rolls). For continuous data, mode is often meaningless and we report 'none' if no value repeats.
Standard deviation: typical distance from the mean. Same units as your data. Two-thirds of values typically fall within ±1 standard deviation of the mean (for normal distributions).
Sample vs population
If your numbers are the entire population (every employee in your company, every day of a month), use population standard deviation: divide by n. We toggle this off when you uncheck 'Sample standard deviation'.
If your numbers are a sample drawn from a larger population (a survey of 100 from 10,000 customers), use sample standard deviation: divide by n−1 (Bessel's correction). This is the default and is what most statistics courses and software default to.
The difference shrinks as n grows. For n=100 the two differ by 0.5%; for n=10 they differ by 5%. For very small samples, the choice matters.
Quartiles and the IQR
Q1 (first quartile, 25th percentile) is the median of the lower half. Q3 (third quartile, 75th percentile) is the median of the upper half. The interquartile range (IQR = Q3 − Q1) describes the middle 50% of your data and is robust to outliers.
Box plots use these: the box spans Q1 to Q3, with the median as a line inside. Whiskers extend to the most extreme values within 1.5 × IQR; anything beyond is plotted as outliers.
Frequently asked questions
›How many numbers can I paste?
Up to about 100,000 reasonably. Beyond that the browser may slow. For massive datasets use a programming tool.
›What if I have decimal numbers?
Use a period (.) as the decimal separator regardless of your locale: 3.14, not 3,14.
›Why is the mode 'none'?
Because no value repeats. Mode is only meaningful when at least one value appears two or more times.
›Should I use sample or population for my class data?
If you're treating your class as a sample of the school, use sample (n−1). If your class IS the population, use population (n).
›What's the difference between standard deviation and variance?
Variance is the average squared distance from the mean; standard deviation is its square root. Standard deviation is in the same units as your data, which is why we report both but standard deviation is usually more useful.
›Why does Q1 differ from what my calculator gives?
Different methods exist (Method 1, Method 2, R-default, Excel-default). We use the median-of-lower-half method. Most introductory courses use this; spreadsheet QUARTILE() may differ slightly.
›Can I use negative numbers?
Yes. Negative numbers are fully supported.
›Does the data leave my browser?
No. All calculations run locally; nothing is sent to any server.
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