Range Calculator —
min, max, midrange & IQR.

Field guide

What is the range in statistics?

The range is the simplest measure of variability (spread) in a dataset. It tells you how wide your data spans: the distance from the smallest value to the largest. The formula could not be simpler:

Example: The dataset 3, 7, 11, 15, 23, 42 has a minimum of 3 and a maximum of 42. Range = 42 − 3 = 39.

The range captures the total spread of your data in a single number, making it the fastest way to understand how variable your observations are. It appears in reports, grades, temperature readings, stock prices, and just about every quantitative context where data is collected.

Min and max: the building blocks.

The minimum (min) is the smallest value in the dataset. The maximum (max) is the largest. Both are found by sorting the data and reading the endpoints:

• Sort the data ascending: 3, 7, 11, 15, 23, 42
• The first element is the minimum: 3
• The last element is the maximum: 42
• Range = Max − Min = 42 − 3 = 39

For a computer, finding min and max requires a single pass over the data in O(n) time. This calculator does so and displays the sorted list so you can verify the endpoints at a glance.

What is the midrange?

The midrange is the arithmetic average of the minimum and maximum, the midpoint of the full span of the data:

Example: Min = 3, Max = 42. Midrange = (42 + 3) / 2 = 45 / 2 = 22.5.

The midrange is not the same as the median (the actual middle value when the data is sorted) or the mean(the arithmetic average of all values). All three measure “centre” in different ways:

Because the midrange depends only on the extremes, a single outlier can shift it dramatically. If your dataset were 3, 7, 11, 15, 23, 420 (a typo adding a zero to the last value), the midrange jumps from 22.5 to 211.5, while the median barely moves. The midrange is useful when you specifically want to represent the geometric centre of the observable range, not the “typical” value.

Range vs. IQR: outlier sensitivity.

The range’s biggest limitation is that it only uses two data points, the extremes, and is therefore highly sensitive to outliers. A single unusually large or small observation inflates the range, making it look like the data is more spread out than it really is.

The Interquartile Range (IQR) solves this by measuring the spread of the middle 50% of the data. The IQR ignores the outer 25% on each end:

Where Q1 is the 25th percentile (first quartile) and Q3 is the 75th percentile (third quartile). The calculator uses the linear-interpolation method (identical to NumPy and R’s default Type 7) to compute precise quartile values.

Example: For 3, 7, 11, 15, 23, 42:

• Q1 = 8.5 (interpolated between 7 and 11)
• Q3 = 21.5 (interpolated between 15 and 23)
• IQR = 21.5 − 8.5 = 13
• Range = 42 − 3 = 39

If you change 42 to 420, the range becomes 417, but the IQR stays 13. This stability is why box plots (like the one above) use IQR as the central box width and flag outliers separately.

The 1.5 × IQR outlier rule (Tukey fence)

John Tukey’s outlier rule defines potential outliers as values that fall more than 1.5 × IQR below Q1 or above Q3:

Any value outside these fences is flagged as a potential outlier (shown as a point beyond the whiskers in a standard box plot). Values more than 3 × IQR outside the quartiles are considered “extreme outliers.”

Reading the box plot.

The visualization above is a box-and-whisker plot(box plot), the standard chart for displaying the five-number summary of a dataset: min, Q1, median, Q3, max.

• Whiskers: the lines extending to the minimum and maximum values.
• Box: spans Q1 to Q3, representing the middle 50% of the data (the IQR). The wider the box, the more spread the middle half.
• Median line (indigo): the vertical line inside the box. If it sits close to the centre of the box, the middle half of the data is roughly symmetric. If it is pushed toward Q1, the data is right-skewed; toward Q3, it is left-skewed.
• Mean diamond (amber ◆): the mean value. If the mean is to the right of the median, the dataset is pulled up by high values (right skew); if to the left, by low values (left skew).

When to use range and when to use something else.

Use range when:

• You need the simplest possible summary of spread for a small, clean dataset.
• The minimum and maximum are themselves meaningful (temperature extremes, best/worst scores, price ceilings).
• You’re doing a quick sanity check on whether data values seem plausible (e.g., age should not exceed 120; height should not exceed 250 cm).

Prefer IQR when:

• Your dataset may contain outliers or errors that inflate the extremes.
• You’re comparing spreads across different groups and outliers are expected to differ across groups.

Prefer standard deviation when:

• You want a measure of spread that accounts for every value in the dataset, not just the extremes.
• Your data is approximately normally distributed and you need a spread estimate for further inference (confidence intervals, hypothesis tests).

For deeper statistical analysis including mean, variance, and standard deviation, see the Standard Deviation Calculator.

Disclaimer

Results are computed in the browser with no data sent to any server. Quartile values follow the linear-interpolation method (equivalent to NumPy’s default and R’s type-7 quantile). Input is capped at 1,000 values.