Statistics calculator
Paste or type a list of numbers to get every descriptive statistic at once: mean, median, mode, range, quartiles, variance, standard deviation and outliers, with a box plot.
Box = Q1 to Q3, bar = median, triangle = mean, circles = outliers.
Z-score and percentile calculator
How unusual is one value? The z-score counts how many standard deviations it sits from the mean; for normally distributed data, it converts straight to a percentile.
Shaded area = share of a normal distribution below x. The empirical rule: about 68% of values lie within ±1σ, 95% within ±2σ and 99.7% within ±3σ.
What standard deviation actually measures
Each dot is a data value. The gold line is the mean; the shaded band is one standard deviation either side. Drag a dot (or focus it and use the arrow keys) away from the others and watch how one far-off value inflates the SD, because distances are squared before they are averaged.
Mean, median and mode: which to report
For symmetric data the three sit close together. When they disagree, the gap tells you something: a mean well above the median signals a long right tail (a few very large values). Reporting both, plus the IQR, is a robust summary that one outlier cannot distort.
For spread, see the dedicated standard deviation calculator, which shows the full working table.
Show me the steps
An AI tutor walks through the working for any problem you type. The answer above is computed in your browser; the explanation is optional and is the only thing that leaves your device.
Questions people ask
What is the difference between mean, median and mode?
The mean is the arithmetic average (sum ÷ count). The median is the middle value once the data is sorted (the average of the two middle values for an even count). The mode is the most frequent value; a data set can have several modes or none.
Which is better, mean or median?
Use the median when the data is skewed or has outliers, such as incomes or house prices, because one extreme value drags the mean. Use the mean for roughly symmetric data, where it uses every value.
How are quartiles calculated here?
With the median-of-halves method taught in most school courses and used by TI-84 calculators: split the sorted data at the median (excluding it when the count is odd) and take the median of each half. Excel’s QUARTILE.INC uses interpolation and can give slightly different values.
How are outliers detected?
With Tukey’s fences: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged. It is a rule of thumb, not proof that a value is wrong.
How do I calculate statistics for a data set?
Paste the numbers into the box. For the mean, add them and divide by the count; for the median, sort them and take the middle; for variance, average the squared distances from the mean (dividing by n − 1 for a sample); the standard deviation is the square root of the variance. Every one of these is shown above.
How do I calculate variance?
Subtract the mean from each value, square the results, add them up, and divide by n − 1 (sample) or N (population). For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, the sum of squares is 32, the population variance is 32/8 = 4 and the sample variance is 32/7 ≈ 4.571.
What is a z-score?
z = (x − μ) / σ: how many standard deviations a value lies above (positive) or below (negative) the mean. A z of 1.5 means 1.5 SD above average; for normal data that is about the 93rd percentile.
Do I need a TI-84 for statistics?
Not for descriptive statistics: this page gives the same mean, median, quartiles (TI-84 method), standard deviation and variance. Check your course or exam rules for which handheld you may use in tests; the College Board publishes an approved-calculator list for the SAT and AP exams.
Is my data uploaded?
No. The statistics are computed in your browser. Your last data set is kept in this browser’s localStorage so it is there when you come back; clear it with the Clear button or on the privacy page.