What the statistics calculator reports
The statistics calculator gives the centre, the spread and the shape of your data in one pass. Centre is the mean (the arithmetic average) and the median (the middle value); spread is the range, the standard deviation, the variance and the interquartile range.[1][2]
| Statistic | Formula or rule | Value |
|---|---|---|
| Mean | Σx ÷ n | 82.3333 |
| Median | middle value of the sorted list (average of the two middle values when n is even) | 85 |
| Mode | most frequent value | 85 (appears 3 times) |
| Range | max − min | 29 (66 to 95) |
| Sample standard deviation s | √(Σ(x − mean)² ÷ (n − 1)) | 9.208 |
| Population standard deviation σ | √(Σ(x − mean)² ÷ n) | 8.816 |
| Sample variance s² | Σ(x − mean)² ÷ (n − 1) | 84.7879 |
| Q1 / Q3 (median of halves) | median of the lower / upper half | 75 / 89 |
| Interquartile range | Q3 − Q1 | 14 |
| Standard error of the mean | s ÷ √n | 2.6581 |
| Mean absolute deviation | Σ|x − mean| ÷ n | 7.4444 |
| Skewness G1 | adjusted Fisher–Pearson coefficient | -0.487 |
Use the sample formulas (divide by n − 1) when your numbers are a sample from a larger group, which is the usual case in homework and research. Use the population formulas only when the list is every member of the group you care about. The standard deviation calculator shows each squared difference, step by step.
Mean, median and mode: which one to report
Report the mean for roughly symmetric data and the median when the data are skewed or contain outliers. The mean uses every value, so one extreme number pulls it; the median only cares about order.[3] In the list 12, 15, 14, 13, 16, 15, 14, 58, the mean is 19.63 but the median is 14.5: the single 58 drags the mean far above every other value.
The mode is the only measure of centre that works for categories (most common eye colour, most chosen answer). A list can have one mode, several modes, or none at all when no value repeats; the calculator lists every value tied for the highest count.
Skewness: is the data lopsided?
Skewness measures how lopsided the data are: 0 for a symmetric set, positive when a long tail stretches to the right, negative when it stretches to the left. The calculator reports the adjusted Fisher–Pearson coefficient G1, the version in the NIST handbook and in Excel’s SKEW function.[7] The example scores have G1 = -0.487: a slight left skew from the two lowest scores. The list with the outlier 58 has G1 = 2.79, a strong right skew, which is also why its mean sits far above its median.
Quartiles and the five-number summary
The five-number summary is the minimum, Q1, the median, Q3 and the maximum, and it is what a box plot draws. For the example scores it is 66, 75, 85, 89 and 95.
Quartiles have more than one textbook definition, so two tools can disagree on the same data. This calculator defaults to the method in most introductory courses and on TI-84 calculators: split the sorted list at the median (leaving the median out when n is odd) and take the median of each half.[3] The other option matches Excel’s QUARTILE.INC, which interpolates between data points:[6] for the example it gives Q1 = 76.5 and Q3 = 88.5 instead of 75 and 89. If your class uses a specific calculator, pick the matching method.
How the calculator finds outliers
A value is flagged as a possible outlier when it lies more than 1.5 × IQR below Q1 or above Q3.[3][5] For 12, 15, 14, 13, 16, 15, 14, 58, Q1 = 13.5, Q3 = 15.5 and IQR = 2, so the fences are 10.5 and 18.5, and 58 is outside them. A flag is a prompt to check the value, not a reason to delete it: it may be a typing error, or it may be the most interesting point in the data.
Pasting from a spreadsheetCopy a column from Excel or Google Sheets and paste it into the box: new lines, commas, spaces and semicolons all work as separators. Words and blank cells are skipped and listed under the result, so you can see what was left out.
Common statistics mistakes
- Using the population SD for a sample. Dividing by n instead of n − 1 makes the spread look smaller than it is, especially for small samples.
- Averaging percentages from groups of different sizes. Weight each group by its size first; the weighted grade calculator does exactly this for grades.
- Comparing quartiles from two different tools. Check which quartile method each one uses before deciding one is wrong.
- Reading the mean as “typical” for skewed data. Income, house prices and reaction times are skewed; report the median beside the mean.
Next steps with the same numbers: turn one value into a z-score, build a confidence interval for the mean, or compare two groups with the t-test calculator. Studying for the exam? The AP Stats score calculator estimates your 1–5.
How we check this calculator
The formulas follow the NIST/SEMATECH e-Handbook of Statistical Methods and OpenStax Introductory Statistics.[2][4] Automated tests run before every update: the data set 2, 4, 4, 4, 5, 5, 7, 9 must give a population SD of exactly 2 and a sample SD of 2.13809; 1 to 9 must give quartiles 2.5 and 7.5 by the median-of-halves rule and 3 and 7 by QUARTILE.INC; sums use compensated addition so 0.1 + 0.2 + 0.3 is exactly 0.6.
- 14 November 2026: page and calculator published.
More statistics calculators
- Standard deviation calculatorSample and population SD, step by step
- Z-score calculatorz, percentile and area under the normal curve
- P-value calculatorFrom z, t, chi-square or F
- Confidence interval calculatorMeans and proportions, t or z
- t-test calculatorOne-sample, Welch, pooled and paired
- Binomial distribution calculatorExactly, at most, at least x successes
Frequently asked questions
How do I find the mean, median and mode?
Mean: add the numbers and divide by how many there are. Median: sort them and take the middle value (or the average of the two middle values). Mode: the value that appears most often. For 72, 85, 90, 66, 85, 93, 78, 88, 85, 70, 95, 81 they are 82.33, 85 and 85.
What is the difference between sample and population standard deviation?
The sample standard deviation divides the sum of squared differences by n − 1, the population standard deviation by n. Use the sample version when your data are a sample from a larger group; it corrects for the fact that a sample tends to understate the spread.
How do you calculate the interquartile range?
Subtract the first quartile from the third: IQR = Q3 − Q1. It is the spread of the middle half of the data. For the example scores, 89 − 75 = 14.
Why does my calculator give different quartiles?
There are several accepted quartile methods. TI-84 calculators and most textbooks use the median of each half; Excel’s QUARTILE.INC interpolates. Both are correct for their definition; choose the method your class uses in the calculator’s second step.
How many numbers can I enter?
Up to 10,000 numbers. Everything is calculated in your browser, and nothing you type is sent to us.