Statistics Calculator
Paste any list of numbers to get the mean, median, mode, range, quartiles, IQR, outliers, variance and standard deviation (sample and population).
What is a statistics calculator?
This statistics calculator gives you the common descriptive statistics for a list of numbers in one step: the mean, median and mode; the minimum, maximum and range; the quartiles (Q1 and Q3), the interquartile range and any outliers; and the variance and standard deviation in both their sample and population forms. Separate your numbers with commas, spaces, semicolons or line breaks — a column pasted straight from a spreadsheet works.
It covers the same summary a TI-84 produces with 1-Var Stats and uses the same method for quartiles, so the results line up with what most US textbooks and AP Statistics expect. Use it for homework, lab measurements, survey answers, test scores, or a quick check on a spreadsheet.
The numbers fall into two groups. Measures of center — mean, median and mode — describe a typical value. Measures of spread — range, interquartile range and standard deviation — describe how far the values stray from that center. Describing data honestly usually takes one of each, and the worked examples below show how to choose.
Formula
- Mean x̄ = Σx ÷ n — the sum of the values divided by how many there are.
- Median — the middle value of the sorted list; with an even number of values, the average of the two middle ones.
- Mode — the value or values that occur most often. A list can have no mode, one mode, or several.
- Range = maximum − minimum.
- Quartiles — Q1 is the median of the lower half of the sorted data and Q3 the median of the upper half. When n is odd, the overall median is left out of both halves; this is the method TI-84 1-Var Stats uses. Spreadsheet functions such as Excel's QUARTILE.INC interpolate instead and can give slightly different values.
- Interquartile range IQR = Q3 − Q1, the spread of the middle 50% of the data.
- Outliers — values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR (the "inner fences" in Tukey's rule).
- Sample variance s² = Σ(x − x̄)² ÷ (n − 1), and sample standard deviation s = √s².
- Population variance σ² = Σ(x − μ)² ÷ n, and population standard deviation σ = √σ².
Sample or population?
Use the population formulas only when your numbers are every member of the group you care about — every student in one class, every sale last month. When the numbers are a sample used to describe a larger group, use the sample formulas: dividing by n − 1 instead of n (Bessel's correction) offsets a sample's tendency to underestimate the true spread. If you are unsure, report the sample standard deviation; it is the default in most software and textbooks.
Worked example
Example 1: ten test scores
Data: 5, 8, 12, 15, 20, 22, 25, 28, 30, 35 (n = 10, already sorted).
- Mean: 200 ÷ 10 = 20
- Median: the 5th and 6th values are 20 and 22, so the median is 21
- Mode: none — every value appears once
- Range: 35 − 5 = 30
- Quartiles: lower half 5, 8, 12, 15, 20 gives Q1 = 12; upper half 22, 25, 28, 30, 35 gives Q3 = 28; IQR = 16
- Outliers: the fences are 12 − 1.5 × 16 = −12 and 28 + 1.5 × 16 = 52, so there are none
Standard deviation, step by step:
- Subtract the mean from each value: −15, −12, −8, −5, 0, 2, 5, 8, 10, 15.
- Square the differences: 225, 144, 64, 25, 0, 4, 25, 64, 100, 225. Their sum is 876.
- Sample variance: 876 ÷ 9 = 97.3333, so the sample standard deviation is √97.3333 ≈ 9.8658.
- Population variance: 876 ÷ 10 = 87.6, so the population standard deviation is √87.6 ≈ 9.3595.
Example 2: how one outlier moves the mean
Data: 10, 12, 12, 13, 14, 15, 16, 40 (n = 8).
- Mean = 132 ÷ 8 = 16.5, median = (13 + 14) ÷ 2 = 13.5, mode = 12.
- Q1 = 12, Q3 = 15.5 and IQR = 3.5. The upper fence is 15.5 + 1.5 × 3.5 = 20.75, so 40 is an outlier.
- Sample standard deviation ≈ 9.6806.
Take the 40 out and the mean drops to 13.1429 and the sample standard deviation to 2.0354, while the median barely moves (13). One extreme value moved the mean by more than three points and nearly quintupled the standard deviation. That is why skewed data such as incomes, house prices or response times is usually summarized with the median and IQR rather than the mean and standard deviation.
How to use this calculator
- Paste or type your numbers into the box. Commas, spaces, semicolons and new lines all work as separators, so a column copied from Excel or Google Sheets can go straight in.
- The results update as you type. Anything that is not a number is skipped, so check that Count matches the number of values you expected.
- Choose the right spread: the sample standard deviation for a sample, the population standard deviation for a complete group (see "Sample or population?" above).
- Scan Sorted data and Outliers for typing mistakes — a misplaced decimal point usually shows up at one end of the sorted list.
Negative numbers and decimals are fine (−2.5, 0.75). Do not use commas as thousands separators: 1,250 is read as two numbers, 1 and 250. Remove them first, or separate values with spaces or new lines.
Which statistics should I report?
- Roughly symmetric data without outliers (heights, many test scores): the mean and standard deviation.
- Skewed data or data with outliers (incomes, prices, waiting times): the median and interquartile range.
- Repeated values or categories (shoe sizes, 1–5 ratings): the mode is often the most useful single number.
Learn more in mean vs median vs mode, standard deviation explained and the 68-95-99.7 rule. For standard deviation on its own, use the standard deviation calculator.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods — Measures of location (mean, median, mode)
- NIST/SEMATECH e-Handbook of Statistical Methods — Measures of scale (variance, standard deviation, range, interquartile range)
- NIST/SEMATECH e-Handbook of Statistical Methods — What are outliers in the data? (inner and outer fences)
Frequently asked questions
When should I use the median instead of the mean?
When the data is skewed or has outliers. In Example 2 above, one value of 40 pulls the mean up to 16.5 while the median stays at 13.5, much closer to the typical value. That is why incomes, house prices and response times are usually reported as medians.
What is the difference between sample and population standard deviation?
The population standard deviation divides the sum of squared differences by n; the sample standard deviation divides by n − 1. Use the population version only when your data is the entire group you are describing, and the sample version when it is a sample from a larger group. For the ten scores in Example 1 they are 9.3595 and 9.8658.
Why are my quartiles different from Excel or another calculator?
There are several accepted ways to calculate quartiles. This calculator takes the median of each half of the data, leaving out the overall median when the count is odd — the TI-84 method. For 1, 2, 3, 4, 5, 6, 7 it gives Q1 = 2 and Q3 = 6, while Excel's QUARTILE.INC interpolates and gives 2.5 and 5.5. Neither is wrong; use the method your course or textbook uses.
How are outliers identified?
With the 1.5 × IQR rule: any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged. An outlier is not automatically an error — check whether it is a typing mistake, a measurement problem, or a genuine extreme value before deciding whether to leave it out.
What does "no mode" mean?
Every value appears exactly once, so no value is more frequent than another. If two or more values tie for most frequent, the data is bimodal or multimodal, and all of them are listed.
Does this match the TI-84 1-Var Stats output?
Yes for everything it shows: x̄ is the mean, Σx the sum, Sx the sample standard deviation, σx the population standard deviation, n the count, and minX, Q1, Med, Q3 and maxX the five-number summary, calculated with the same quartile method. The TI-84 also lists Σx², the sum of the squared values, which this calculator does not show.
Can I paste data from Excel or Google Sheets?
Yes. Copy a column or a row and paste it into the box; line breaks and tabs work as separators. Remove thousands separators first, because a comma is treated as a separator — 1,250 would be read as 1 and 250.
How precise are the results?
Calculations use double-precision arithmetic, accurate to about 15 significant digits, and the results are shown rounded to 4 decimal places. Round only at the end of your own calculation to avoid accumulating rounding errors.