Range Calculator
Get the range and a full suite of descriptive statistics for any data set. Paste your numbers separated by commas (or spaces), choose sample or population, and instantly see the range, min, max, mean, median, mode, quartiles, IQR, standard deviation, variance, and more, with a step-by-step breakdown.
Formula
Worked example
For 12, 7, 19, 4, 23: sorted = 4, 7, 12, 19, 23. Min = 4, max = 23, range = 19. Mean = 65/5 = 13. Sample variance = [(81+36+1+36+100)/4] = 63.5. Std dev = 7.969. Q1 = 7, Q3 = 19, IQR = 12.
What the range tells you
The range is the most direct measure of how spread out a data set is. You find it by subtracting the smallest value from the largest, giving the total distance the data covers along the number line. A small range means values are tightly clustered; a large range means they are stretched far apart. Because it takes just one subtraction, the range is the quickest way to summarise variability and is usually the first spread statistic taught alongside the mean and median.
Why the range alone can mislead
The range depends entirely on the two most extreme values, so it ignores everything in between. This makes it highly sensitive to outliers: a single unusually large or small number can inflate the range even when the rest of the data is tightly packed. Two data sets can share the same range yet have completely different distributions. For that reason, this calculator also shows the interquartile range (IQR), standard deviation, and mean absolute deviation (MAD), which capture the typical spread across all values.
Interquartile range and quartiles
The interquartile range is Q3 minus Q1, where Q1 is the value below which 25% of data falls and Q3 is the value below which 75% falls. Because it uses only the middle half of the data, the IQR is robust to outliers, making it the preferred spread measure for skewed distributions or data with extreme values. Q2 is the median. Together, Q1, Q2, Q3 and the IQR form the five-number summary that underlies a box plot.
Standard deviation and variance
Variance measures the average squared distance of each point from the mean. Standard deviation is the square root of variance, restoring the original units so you can compare it directly to the data. When your numbers are a sample from a larger population, divide by n-1 (Bessel's correction) to get an unbiased estimate; if you have the full population, divide by n. This calculator shows both options via the "Data type" toggle.
Outlier detection with Tukey fences
This calculator uses Tukey fences to flag potential outliers. The lower fence is Q1 minus 1.5 times the IQR, and the upper fence is Q3 plus 1.5 times the IQR. Any value outside these fences is a mild outlier; values beyond Q1 minus 3*IQR or Q3 plus 3*IQR are extreme outliers. Spotting them early explains why the range may be unexpectedly large compared to the IQR.
How to enter your data
Type or paste your numbers into the box separated by commas, spaces, or a mix of both. Values copied straight from a spreadsheet column work without any cleanup. Anything that is not a valid number is skipped, so stray text will not break the result. All statistics update in real time as you edit, and the sorted data table at the bottom shows every value alongside its deviation from the mean.
Spread measures compared
| Measure | Formula | Sensitive to outliers? | Best used when |
|---|---|---|---|
| Range | max - min | Yes (extreme) | Quick check; data has no outliers |
| IQR | Q3 - Q1 | No | Skewed data or data with outliers |
| Std deviation | sqrt(variance) | Moderate | Symmetric, roughly normal data |
| Variance | avg. squared deviation | Moderate | Inputs to further calculations |
| MAD | avg. |x - mean| | Less than std dev | Robust alternative to std dev |
| Mid-range | (max + min) / 2 | Yes | Simple central-value estimate |
All measures of spread have trade-offs. Use this table to choose the right one for your data.
Frequently asked questions
What is the range in statistics?
The range is the difference between the largest and smallest values in a data set: range = max - min. It is the simplest measure of spread (variability), telling you the total width the data covers. It is quick to compute but sensitive to outliers.
Can the range be negative or zero?
The range can never be negative, because the maximum is always at least as large as the minimum. It is zero only when every value in the data set is identical, meaning there is no spread at all.
What is the difference between range and IQR?
The range uses only the two most extreme values, so a single outlier can make it very large. The interquartile range (IQR = Q3 - Q1) uses only the middle 50% of the data, making it robust to outliers. For skewed distributions or data with extreme values, the IQR is a more reliable measure of typical spread.
When should I use sample versus population standard deviation?
Use sample standard deviation (divides by n-1) when your data is a subset drawn from a larger group and you want to estimate the population spread. Use population standard deviation (divides by n) when your data represents the entire group of interest. In most everyday situations, "sample" is the correct choice.
How is the mean absolute deviation (MAD) different from standard deviation?
Both measure the average distance of data points from the mean. Standard deviation uses squared differences (which penalises large deviations more), then takes the square root. MAD uses absolute differences, making it more resistant to outliers. MAD is always less than or equal to the standard deviation.
What are Tukey fences and how do they detect outliers?
Tukey fences are boundaries used to flag potential outliers. The lower fence is Q1 minus 1.5 times the IQR; the upper fence is Q3 plus 1.5 times the IQR. Any data point outside these fences is considered a mild outlier. Values beyond 3 times the IQR from the quartiles are extreme outliers. This method is the basis of the classic box-and-whisker plot.