Descriptive Statistics
Range Calculator
The range is the distance from the smallest value to the largest, and the coefficient of range scales that distance by the sum of the extremes.
Worksheet
Press Calculate to see the result.
The range is the distance from the smallest value to the largest, and the coefficient of range scales that distance by the sum of the extremes.
What this calculator answers
Five temperature readings are 18, 22, 25, 31, and 40. Only 18 and 40 decide the range. The three middle readings could shift a little and the range would not move at all. That makes the range easy to explain and easy to break: one bad sensor at either end rewrites it. The coefficient of range then asks how large that gap is compared with the sum of the two extremes, which is useful when you want a unit-free look at the same two numbers.
The headline is maximum minus minimum. The coefficient of range is that difference divided by maximum plus minimum, and it is withheld when those extremes sum to zero. Supporting counts and intermediate terms sit under the headline so a reader can see what was divided by what. When a checkbox or a tail setting changes the divisor or the rejection region, that choice appears in the steps rather than vanishing into a silent default.
The formula, written out
Range and coefficient of range uses this relationship.
range = max - min. coefficient = (max - min) / (max + min), when max + min is not 0.
- min. Smallest typed value.
- max. Largest typed value.
- range. Maximum minus minimum, in the unit of the data.
- coefficient. Range divided by the sum of the extremes.
Subtracting the extremes keeps the unit and ignores every interior point. Dividing by the sum of the extremes cancels the unit and blows up if the extremes are equal in size and opposite in sign. The algebra is the named textbook identity for this worksheet. Intermediate products and quotients appear in order so a calculator and a pencil can agree to the displayed rounding. If a neighbouring page uses a different divisor or a continuity correction, that page says so on its own ticket.
A full worked example
Example loaded in the worksheet
The form is prefilled with a small example so every arithmetic step can be checked by hand. Change one field after you finish the walkthrough and confirm the ticket moves the way the formula predicts.
The values are 18, 22, 25, 31, 40. The minimum is 18 and the maximum is 40. The range is 40 minus 18, which equals 22.
Values strictly between the extremes do not enter that subtraction. The sum of the extremes is 40 + 18 = 58. The coefficient of range is 22 / 58 = 0.3793.
The range keeps the unit of the data. The coefficient does not. There are 5 typed values, and only two of them set the range unless several share an extreme.
| Range | 22 |
|---|---|
| Coefficient of range | 0.3793 |
| Minimum | 18 |
| Maximum | 40 |
A second situation
The warmest reading rises from 40 to 60
The values are 18, 22, 25, 31, 60. The minimum is 18 and the maximum is 60. The range is 60 minus 18, which equals 42.
Values strictly between the extremes do not enter that subtraction. The sum of the extremes is 60 + 18 = 78. The coefficient of range is 42 / 78 = 0.5385.
The range keeps the unit of the data. The coefficient does not. There are 5 typed values, and only two of them set the range unless several share an extreme.
| Range | 42 |
|---|---|
| Coefficient of range | 0.5385 |
| Minimum | 18 |
| Maximum | 60 |
Replacing 40 with 60 leaves the minimum at 18 and lifts the range from 22 to 42. The coefficient of range rises from 0.3793 to 0.5385 because the gap grew faster than the sum of the extremes. The second example changes the feature that this formula is sensitive to, and the ticket shows the new figure beside the same definition. That contrast is the fastest way to see which input owns the movement.
What moves when the input moves
The largest reading changed from 40 to 60. The smallest stayed at 18. The headline result went from 22 to 42.
The nudged inputs
The values are 18, 22, 25, 31, 60. The minimum is 18 and the maximum is 60. The range is 60 minus 18, which equals 42.
Values strictly between the extremes do not enter that subtraction. The sum of the extremes is 60 + 18 = 78. The coefficient of range is 42 / 78 = 0.5385.
The range keeps the unit of the data. The coefficient does not. There are 5 typed values, and only two of them set the range unless several share an extreme.
| Range | 42 |
|---|---|
| Coefficient of range | 0.5385 |
| Minimum | 18 |
| Maximum | 60 |
How to read the result
A range of 22 degrees says nothing about whether the readings clustered near 18 or spread evenly up to 40. The coefficient 0.3793 is a ratio, so it has no degree sign. Say the unit, the sample size or contract terms, and the formula name in the same sentence as the figure. A number without those three pieces invites a later reader to invent a definition that this page never used.
Write the result with its unit, the inputs that produced it, and the name of the formula. Write the result with its unit, the inputs that produced it, and the name of the formula. If the ticket shows a decision sentence, quote the alpha and the tail with it. If the ticket shows a money or dose figure, quote the rate and the schedule that produced it.
Assumptions that have to stay true
- The minimum and maximum were measured on the same scale.
- Both extremes are real observations, not sentinels for missing data.
- A coefficient is wanted only when the sum of the extremes is not zero.
- Interior points are allowed to be irrelevant to this particular summary.
If an assumption above is false, do not average the discomfort away. Change the worksheet or change the question. A correct arithmetic step on the wrong model is still the wrong answer for the decision you are trying to make.
Mistakes that change the answer
- Averaging the range of several groups that have different counts.
- Using the range as a typical deviation from the mean.
- Computing the coefficient when the extremes sum to zero and reporting a huge quotient from rounding.
- Forgetting that one new extreme replaces the range completely.
Where a different calculator is the honest choice
Use the interquartile range when the outer quarter on each side should not set the spread. Use the midrange calculator when you want the halfway point between the extremes rather than the gap. Use descriptive statistics when the range should sit beside the quartiles. Related links under the essay open pages that keep their own formulas instead of hiding a mode switch inside this ticket.
When the job changes, move to a page built for that job: Midrange Calculator, Interquartile Range Calculator, Descriptive Statistics Calculator.
Check yourself
Readings are 18, 22, 25, 31, and 40. What is the range, and what is the coefficient of range?
The range is 22 and the coefficient of range is 0.3793.
Using the result in a sentence
Daily high-low temperatures, the span of a price series, and the gap between the best and worst trial are range questions. Keep the count, the unit, and the assumption list beside any copy of the number that leaves this browser tab.
Two readings determine this whole page. A single corrupted endpoint is enough to mislead a control limit. Prefer a quartile spread when the tails are noisy. Pair the headline with the steps before you staff a route, set a grade boundary, or compare two contracts from a single number.
Questions people ask next
01What definition does the Range Calculator commit to?
This page uses Range and coefficient of range: range = max - min. coefficient = (max - min) / (max + min), when max + min is not 0.. Subtracting the extremes keeps the unit and ignores every interior point. Dividing by the sum of the extremes cancels the unit and blows up if the extremes are equal in size and opposite in sign. If a textbook uses a different divisor, a different continuity correction, or a different rounding rule, the last digits can move, so the definition is printed above the result. The worksheet asks for Numbers, and it refuses a blank that the formula cannot interpret. Keep that printed definition in the sentence you write next to the figure so a later reader can rebuild the arithmetic without guessing which convention you chose.
02How should the worked example be read out loud?
In the loaded example the range is 22. A range of 22 degrees says nothing about whether the readings clustered near 18 or spread evenly up to 40. The coefficient 0.3793 is a ratio, so it has no degree sign. Say the unit and the count before you say whether the number is large or small. Read the steps in order rather than jumping to the headline, because the intermediate terms are where a swapped percent and proportion usually hide. If the ticket shows both a primary figure and a comparison figure, name which one you are quoting.
03What is the fastest way to get a misleading result?
Averaging the range of several groups that have different counts. Two readings determine this whole page. A single corrupted endpoint is enough to mislead a control limit. Prefer a quartile spread when the tails are noisy. A second common failure is leaving a checkbox or tail setting in the wrong state and then treating the number as if the default had matched your plan. Reset the example, change one input, and confirm the ticket moves in the direction the formula predicts before you trust a live run.
04When should I leave this page for a different calculator?
Use the interquartile range when the outer quarter on each side should not set the spread. Use the midrange calculator when you want the halfway point between the extremes rather than the gap. Use descriptive statistics when the range should sit beside the quartiles. The related links under the essay go to those worksheets, which keep their own formulas instead of hiding them in a mode switch. If the question changed from a summary to a test, from a payment to a refinance, or from a raw score to a percentile, switch pages rather than forcing this ticket to answer a job it was not built for.
05What belongs in the sentence next to the number?
The range is 22 and the coefficient of range is 0.3793. Name the formula, the sample size or the inputs, and the unit before you compare the figure with someone else's. A bare number without those three pieces cannot be audited when a score, a rate, or a lab value is challenged later. Store the inputs beside the result whenever the figure will travel into a report.