Statistics Calculator
Get a full descriptive-statistics summary from any list of numbers — count, mean, median, mode, range, variance, standard deviation, mean absolute deviation, and quartiles — in one place.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Count
10
Sum
223
Mean
22.3
Median
21.5
Mode
15
Range
23
Variance (sample)
58.0111
Std Dev (sample)
7.6165
Mean Abs. Deviation
6.16
Example
For these 10 numbers: mean = 22.3, median = 21.5, mode = 15, range = 23, sample standard deviation = 7.6165, and an interquartile range (IQR) of 14 (Q1 = 15, Q3 = 29).
Five-number summary: Min, Q1, Median, Q3, Max
What is a Statistics Calculator?
A statistics calculator summarizes an entire data set with a handful of numbers that describe its center, spread, and shape. This tool computes the full set at once — measures of center (mean, median, mode), measures of spread (range, variance, standard deviation, mean absolute deviation), and the quartiles that divide your data into four equal parts.
It's built for anyone who needs more than a single average: students checking homework, analysts doing a quick sanity check on a data set, or anyone who wants the full five-number summary (minimum, Q1, median, Q3, maximum) visualized at a glance.
Quartiles & Sorted Data
Q1 (25th percentile)
15
Q3 (75th percentile)
29
IQR (Q3 − Q1)
14
Sorted values:
12, 15, 15, 18, 21, 22, 25, 29, 31, 35
Key Formulas
Variance and standard deviation come in two flavors. Use the sample formula (dividing by n − 1) when your numbers are a sample drawn from a larger population — this is the far more common case and slightly inflates the result to correct for the fact that a sample tends to underestimate the true population spread. Use the population formula (dividing by n) only when your list truly is the entire population you care about.
Quartiles and the IQR
Quartiles split a sorted data set into four equal-sized groups. Q1 is the median of the lower half of the data, Q3 is the median of the upper half, and the median itself (Q2) splits the two halves. The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of the data and is far less sensitive to extreme outliers than the range, which only looks at the two most extreme values.
Standard Deviation vs. Mean Absolute Deviation
Both measure how spread out your data is around the mean, but standard deviation squares each deviation before averaging (which penalizes large deviations more heavily and matches the math behind the normal distribution), while mean absolute deviation simply averages the absolute distance from the mean. MAD is more intuitive to interpret but standard deviation is far more widely used in statistical theory and testing.
Example — Your Current Inputs
For these 10 numbers: mean = 22.3, median = 21.5, mode = 15, range = 23, sample standard deviation = 7.6165, and an interquartile range (IQR) of 14 (Q1 = 15, Q3 = 29).
Additional Example — Test Scores
A class scores 65, 70, 72, 75, 80, 82, 85, 90, 92, 95 on a test. The mean is 80.6, the median is 81, there's no repeated mode, and the range is 30. Q1 is 72, Q3 is 90, giving an IQR of 18 — a much tighter picture of the "typical" spread than the full 30-point range, since it ignores the lowest and highest scorers.
About These Parameters
- Numbers
- Your full data set, separated by commas, spaces, or line breaks. Decimals and negative numbers are both supported.
- Standard Deviation Type
- Sample (dividing by n − 1) is correct almost anytime you're analyzing a subset of a larger group. Population (dividing by n) is only correct when your list is the complete population itself, with nothing left out.
Frequently Asked Questions
Why does my variance change when I switch from sample to population?
Sample variance divides by n − 1 instead of n, which makes it slightly larger — this correction (Bessel's correction) compensates for the tendency of a sample to underestimate the true spread of the full population it was drawn from.
What's the difference between range and IQR?
Range only looks at the highest and lowest values, so a single outlier can inflate it dramatically. IQR looks only at the middle 50% of the data, making it a much more robust measure of typical spread when outliers are present.
Can a data set have more than one mode?
Yes — if two or more values tie for the highest frequency, the data set is multimodal, and this calculator lists every tied value. If every value appears only once, there is no mode at all.
How are quartiles calculated when the count doesn't divide evenly?
This calculator uses the common "exclusive" method: it splits the sorted data into a lower and upper half (excluding the overall median itself when the count is odd), then takes the median of each half as Q1 and Q3. Other conventions exist and can give slightly different quartile values for the same data.