Range Calculator

range = max − min

max

The largest value in the data set. Only this one and the smallest value take part in the calculation, so everything between them can be reshuffled freely without changing the answer

min

The smallest value in the data set. Together with the largest it defines the whole span, which is why the range is described as a measure of scale that uses the extremes and nothing else

range

The width of the interval that contains every value, in the same units as the data. It is never negative, and it is zero exactly when every value is identical

n

How many values the list holds, up to 200 here. It changes nothing about the answer — the count is printed only so you can confirm the whole list was read

Reach for the range when you need a spread in one line and the extremes are the interesting part: the day's temperature swing, the spread between the cheapest and dearest quote, the difference between the best and worst time in a race. It is also the honest summary of a process where only the extremes matter, such as a tolerance check — a shaft either fits inside the allowed band or it does not. Where it is the wrong tool is whenever the middle of the data matters. Because it uses two values and discards the rest, a single wild reading moves it as much as a real shift in the whole distribution, which is why the standard deviation and the interquartile range exist: those two spread the influence of the data out, and stay useful when the list has a heavy tail. A range quoted next to a mean is a warning sign unless the list is short; a range quoted next to the smallest and largest values, as above, is simply a description of the two ends.

1. Eight values: the range is 7

   1. Sort: 2, 4, 4, 4, 5, 5, 7, 9 — the smallest value is 2 and the largest is 9
   2. range = 9 − 2 = 7
   3. The six values in between — 4, 4, 4, 5, 5 and 7 — took no part in the calculation

   The eight values happen to sit inside three units of the middle, yet the range reports 7 because it measures the full span, not the crowded part. That gap between 'how wide the list is' and 'how tightly the values cluster' is the whole reason a second measure of spread is usually quoted alongside it.

2. One value pushed out: the range jumps to 88

   1. Only the largest value changed, from 9 to 90 — the other seven are identical to the first example
   2. range = 90 − 2 = 88
   3. The sample standard deviation of the same list is 30.2864, against 2.1381 before

   Both measures rose, but for different reasons. The range moved by exactly the amount the extreme value moved, because it is decided by the two outermost points and by nothing else. The standard deviation is spread across all eight values, so the same single change is absorbed and diluted by the other seven. A reading error of one digit in one number is enough to make a range meaningless; it takes a real change in the data to move the standard deviation that far.

3. Negative values and a decimal

   1. The smallest value is −5 and the largest is 10 — the sign is part of the value, so the span crosses zero
   2. range = 10 − (−5) = 10 + 5 = 15
   3. Negative readings work exactly like positive ones: subtracting the minimum adds its magnitude because the two negatives cancel

   Subtracting a negative number is where hand calculations most often go wrong, and the answer is visibly larger than either endpoint when the data straddles zero. A list of negative temperatures, altitudes below sea level or account balances all behave the same way.

The range uses two values out of the whole list, so a single extreme reading decides it completely: one typing mistake, one instrument glitch, one genuinely unusual day and the number moves by the full amount of the error. It also says nothing about the middle of the data, which is where most of the values usually are — two lists with the same minimum and maximum can be evenly spread or bunched into a single heap, and the range cannot tell them apart. Comparing ranges across data sets is only meaningful when the units and the sample sizes are comparable, since a larger sample has more chances to contain an extreme value. The list is capped at 200 values, and a token such as 1,500 is refused rather than guessed at, because a comma between digits is a decimal point in some countries and a thousands separator in others. This page does not flag outliers: the range is the last measure you would use for that, since it is defined by the very values you would be testing.

How do you find the range of a data set?

Find the largest value and the smallest value, then subtract: range = maximum − minimum. For the list 2, 4, 4, 4, 5, 5, 7, 9 that is 9 − 2 = 7. Nothing else in the list matters, so you do not have to sort the data or count how many values there are — though sorting is a reliable way to spot the two extremes when the list is long. The calculator above takes the numbers as you paste them and prints the minimum and maximum beside the answer so the subtraction can be checked.

Why is the range so easily thrown off by one value?

Because it is defined by the two outermost values and ignores all the others. Change 9 to 90 in the example and the range goes from 7 to 88 — a jump of 81, which is exactly how far that one value moved. The sample standard deviation of the same list only rises from 2.1381 to 30.2864, because each of the eight values contributes a share. That sensitivity is not a defect of the formula; it is what 'the width of the list' means. It does mean a range should never be quoted without saying how many values went into it.

Is the range the same as the interquartile range?

No, and they answer different questions. The range is the full width of the data, from the smallest value to the largest. The interquartile range is the width of the middle half, from the first quartile to the third. The interquartile range is deliberately insensitive to the tails and the range is deliberately sensitive to them, so quoting both gives a reader the full width and the width of the crowded middle in two numbers. If you only have room for one, ask whether an extreme reading in your data is meaningful or an error.

Does the range depend on the sample or population choice?

It does not, and that is why there is no sample/population selector on this page. The distinction matters for quantities that divide by the number of values or by one less than it — the variance and the standard deviation — because that divisor differs between a sample and a whole population. The range is a subtraction, so there is no divisor to disagree about. The variance and standard deviation pages both carry that selector; here it would change nothing, and offering it would suggest otherwise.

Can the range be negative, or zero?

It can never be negative: the largest value is by definition at least as big as the smallest, so the subtraction returns zero or something positive. It is zero exactly when every value in the list is the same, including the case of a single value, where the maximum and minimum are that value and the range is 0. Zero is a real answer here, not a failure — it says the data has no spread at all. A single value is accepted for the same reason: nothing in this calculation needs a second observation.

Does this page tell me which values are outliers?

No. The usual rule for flagging possible outliers is based on the interquartile range — a value more than 1.5 × IQR below the first quartile or above the third — and that is a separate calculator. Using the range for the job would be circular, since the range is defined by the very extreme values you would be testing: every data set's own minimum and maximum are, by definition, its most extreme points. This page describes how wide the list is and leaves the verdict to the tool built for it.

• Measures of Scale — NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.5.6 (defines the range as the largest value minus the smallest, and notes that the spread near the centre of the data is not captured at all) — National Institute of Standards and Technology
• GB/T 3358.1-2009, Statistics — Vocabulary and symbols, Part 1 (the Chinese national vocabulary standard covering the range and the other measures of scale; the record page notes that no online full text is offered) — State Administration for Market Regulation, China