Find the minimum, maximum, range, midrange and interquartile range from raw numbers or a frequency table. You can also calculate an endpoint interval or a grouped class-boundary span. Every result states whether it is exact or estimated.
Range Calculator with Steps
Select the format that matches your information. The calculator validates complete entries, keeps full precision during calculation and processes your data inside the browser.
Maximum 15 minus minimum 4
Endpoint number line
Exact endpointsThe highlighted interval runs from the smallest to the largest entered observation.
Calculated measures
| Measure | Value | Method or meaning |
|---|
Endpoint sensitivity
This comparison shows how much the range changes after removing one occurrence of either endpoint. It does not remove data from the main result.
Ordered data preview
A bounded preview keeps large inputs responsive.
Calculation steps
- Enter valid data and calculate the range.
Recent calculations
Your six latest calculations appear here for this page session.
How to Use This Range Calculator
- Select Raw values, Frequency, Grouped or Endpoints to match the information you have.
- Enter the data in the displayed fields. Raw data accepts a simple list. Table modes require one row per line.
- For raw or frequency data, select the quartile convention used for the optional IQR comparison.
- Choose the displayed precision. The setting changes rounding on screen, not the values used in the calculation.
- Select Calculate range. Review the endpoint number line, supporting measures, sensitivity check and substituted steps.
Raw values accept negative numbers, decimals, scientific notation and simple fractions. For example, -4.5, 1/2 and 2e1 become -4.5, 0.5 and 20. Repeated values remain separate observations. The frequency mode combines duplicate value rows and locates quartiles through cumulative counts without expanding a large table into millions of browser elements.
The calculator rejects incomplete tokens, labels and executable text. It never silently converts invalid content to zero. Your entries remain on the current page and are not sent to a server by this tool.
What Is the Range in Statistics?
The range is the distance between the largest and smallest values in a numerical dataset. It gives a fast summary of the full observed span. If daily temperatures run from 12 degrees to 27 degrees, the range is 15 degrees. If account changes run from -8 to 22, the range is 30 because 22 - (-8) = 30.
Range always uses the numerical endpoints, not their positions in the typed list. Sorting helps reveal those endpoints, but sorting does not change the result. Repeated minimum or maximum values also leave the main range unchanged. They matter only when you study what happens after an endpoint observation is removed.
A range of zero means every included value equals the same number. It does not mean the data is missing. One observation also has a range of zero because its minimum and maximum are identical. Whether a one-value dataset is useful depends on your question, but the endpoint calculation itself is defined.
Range Formula and Worked Example
Let xmin be the minimum and xmax be the maximum. The formula is:
For the values 4, 7, 9, 10, 12 and 15, the smallest value is 4 and the largest is 15.
| Step | Calculation | Result |
|---|---|---|
| Find the minimum | Smallest ordered value | 4 |
| Find the maximum | Largest ordered value | 15 |
| Subtract | 15 − 4 | 11 |
The range is 11 units. The value 11 describes the distance between the endpoints. It is not the number of observations, the number of distinct values or the count of whole numbers in the interval.
Minimum, Maximum, Midrange and Semi-Range
The minimum and maximum identify the observed endpoints. The midrange is the arithmetic midpoint between them. The semi-range is half of the range, so the endpoints can be written as midrange plus or minus semi-range.
For endpoints 4 and 15, the midrange is 9.5 and the semi-range is 5.5. Therefore, the interval is 9.5 ± 5.5. The midrange uses only the same two endpoints as the range. It should not be confused with the arithmetic mean or median, both of which use more information about the dataset.
The coefficient of range is sometimes written as (maximum - minimum) divided by (maximum + minimum). It is most interpretable for nonnegative ratio-scale values with a meaningful zero. The calculator reports it as unavailable when the denominator is zero and adds a caution when signed values make the ratio difficult to interpret.
Raw Values, Frequency Tables, Grouped Classes and Endpoints
| Input mode | What the range represents | Precision | Main caution |
|---|---|---|---|
| Raw values | Maximum observation minus minimum observation | Exact for the entered finite values | A typing error at either endpoint changes the result sharply |
| Frequency table | Largest positive-frequency value minus smallest positive-frequency value | Exact for the supplied counts | Zero-frequency rows must not create endpoints |
| Grouped classes | Upper boundary of the highest active class minus lower boundary of the lowest active class | Class-boundary span | The original minimum and maximum inside those classes are unknown |
| Known endpoints | Entered maximum minus entered minimum | Exact for the stated endpoints | It cannot verify how the endpoints were obtained |
Grouped data needs special care. Suppose the first occupied class is 0 to 10 and the last is 20 to 30. The class-boundary span is 30, but the actual observations might run from 3 to 27, producing a raw range of 24. Because the original endpoints were discarded during grouping, the exact raw-data range cannot be reconstructed. This calculator labels the grouped answer as a class-boundary span and labels its grouped quartiles as estimates.
Range vs Interquartile Range and Standard Deviation
Range is easy to calculate, but it uses only two observations. The interquartile range uses the first and third quartiles and describes the spread of the middle half. Standard deviation summarizes distances around the mean and uses every observation. These measures answer different questions.
| Measure | Formula or basis | Best use | Limitation |
|---|---|---|---|
| Range | Maximum − minimum | Fast full-span check and endpoint limits | One extreme value can dominate it |
| IQR | Q3 − Q1 | Spread of the middle 50 percent | Depends on the selected quartile convention |
| Standard deviation | Square root of average squared deviation | Variation around the mean | Requires a sample or population choice |
| Midrange | (Maximum + minimum) ÷ 2 | Center of a known interval | Ignores all values between the endpoints |
The optional IQR on this page uses either inclusive Type 7 interpolation or the median-of-halves method. Both conventions are used in practice, and small datasets can produce different Q1, Q3 and IQR results. State the selected method when comparing software or showing academic work.
For a broader summary with mean, median, mode, variance, standard deviation, skewness and a box plot, use the Statistics Calculator.
Why Outliers Affect the Range
Consider 2, 3, 4, 5 and 100. The range is 98, even though four of the five values lie between 2 and 5. Replacing 100 with 6 reduces the range to 4. The first result is mathematically correct, but it mainly describes the distance to one extreme observation.
An extreme value is not automatically an error. It might record a rare event, a valid high performer, a machine fault or a data-entry mistake. Check the source, unit, collection method and timestamp before changing it. Report the full range when the endpoint matters. Report IQR, median absolute deviation or standard deviation alongside it when the internal distribution also matters.
The endpoint sensitivity panel removes one occurrence of the minimum and maximum separately and recalculates the range. This is a diagnostic comparison only. The main result always includes every accepted observation. If an endpoint is repeated, removing one occurrence may leave the range unchanged.
Ranges with Negative Numbers, Decimals and Fractions
The formula does not change when values are negative. Always subtract the minimum with its sign. For -8, -3, 4 and 10, the maximum is 10 and the minimum is -8. The range is 10 - (-8) = 18. A common error is to ignore the second negative sign and report 2.
Decimals and fractions are also ordinary numerical endpoints. The values 1/2, 1.25 and 2.75 become 0.5, 1.25 and 2.75, so the range is 2.25. Scientific notation works the same way. For 2e3 and 7.5e3, the range is 5.5e3, or 5,500.
Keep all measurements in one unit before calculating. A span between 2 metres and 350 centimetres is meaningless until both endpoints use metres or both use centimetres. The range keeps the original measurement unit. It does not use a squared unit, unlike variance.
Practical Uses of a Range Calculation
- Education: compare the lowest and highest test score, study time or assignment result.
- Quality control: check the observed span of dimensions, temperatures, cycle times or instrument readings.
- Finance: summarize the high-low span of comparable prices or returns, while recognizing that range alone does not measure risk completely.
- Sports: compare fastest and slowest times, minimum and maximum scores or seasonal performance limits.
- Weather: calculate the daily or monthly temperature range from consistent readings.
- Operations: review shortest and longest delivery, queue or service times before examining the full distribution.
Range is especially useful when limits themselves matter, such as a machine tolerance, an operating temperature interval or a lowest-to-highest price quote. It is less informative when you need the typical spread of most observations. In that case, pair it with IQR or standard deviation.
Common Range Calculation Mistakes
- Subtracting in the wrong order. Use maximum minus minimum, so a valid range is never negative.
- Using the first and last typed values without finding the true numerical endpoints.
- Counting observations or distinct integers instead of measuring endpoint distance.
- Dropping a negative sign when subtracting a negative minimum.
- Treating grouped class boundaries as the exact minimum and maximum observations.
- Allowing a zero-frequency row to create a false endpoint.
- Comparing values in mixed units or different time periods.
- Removing an extreme value only because it produces a wide range.
- Comparing IQR results without checking the quartile convention.
- Using commas as thousands separators when commas already separate entries.
Calculation Method and Review Sources
The definition and limitations of range were reviewed against the NIST measures of scale. The IQR explanation was checked against the NIST interquartile range reference and OpenStax guidance on data location.
The engine finds endpoints from unrounded finite numbers. Frequency and grouped modes use cumulative counts instead of expanding repeated observations. Raw inputs are limited to 50,000 values and tables to 10,000 rows to protect browser responsiveness. Values with absolute magnitude above 1e150 are rejected so endpoint subtraction, midpoint and ratio calculations remain finite and auditable in browser arithmetic.
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Frequently Asked Questions
What is the range of a data set?
The range is the largest value minus the smallest value. It measures the full observed distance between the two endpoints but does not describe how values are distributed inside that interval.
How do I calculate range?
Find the minimum and maximum, then subtract the minimum from the maximum. For 3, 7, 8 and 12, the range is 12 - 3 = 9.
Can a range be zero?
Yes. The range is zero when the minimum equals the maximum. This happens when all included observations have the same value or when the dataset contains one value.
Is range the number of values between the minimum and maximum?
No. Range measures numerical distance, not observation count or the number of integers in an interval. The values 2 and 8 have a range of 6, although the closed integer interval contains seven integers.
How do I find range with negative numbers?
Keep both signs and use maximum minus minimum. For -9, -2 and 4, the range is 4 - (-9) = 13.
What is the difference between range and interquartile range?
Range uses the maximum and minimum and covers the full span. IQR equals Q3 minus Q1 and describes the middle 50 percent, so it is usually less sensitive to extreme endpoints.
How do outliers affect the range?
One unusually low or high observation can widen the range sharply because only the two endpoints determine it. Investigate an extreme value before removing it and compare range with IQR or standard deviation.
How is range calculated from a frequency table?
Use the smallest and largest values with positive frequency, then subtract. Rows with zero frequency do not represent observations and do not create endpoints.
Is grouped-data range exact?
Usually not. Grouped classes hide the original minimum and maximum. The upper boundary of the highest occupied class minus the lower boundary of the lowest occupied class is a class-boundary span, not the exact raw-data range.
What units does the range use?
Range keeps the same unit as the original values. A temperature range measured in degrees stays in degrees. Convert mixed units before calculating.
Calculation and Financial Disclaimer
This free tool provides mathematical summaries for informational and educational use. It does not provide statistical, academic, financial, medical, legal or professional advice. Verify important results, source data, units and method requirements independently.