What is the midrange?
The midrange is the number exactly halfway between the smallest and the largest value in a data set. Add the minimum to the maximum, divide by two, done. For the quiz scores 14, 9, 17, 11, 6, 20 and 12, the smallest is 6 and the largest is 20, so the midrange is 13.
It's the oldest and laziest of the measures of centre, and that's meant as a compliment. You can find it in your head without sorting anything or adding up a long column. You've probably used it without the name, too. When a forecast gives a low of 58°F and a high of 81°F, the "average temperature" for that day is really a midrange: 69.5°F.
The catch is that the midrange only ever looks at two numbers. Every value in between could change and it wouldn't notice. That makes it quick, and it also makes it fragile. One stray value at either end drags it along. That's why statistics courses teach it next to the mean and the median rather than instead of them, and why this page shows all three on your own data.
The Midrange Calculator takes a pasted list of numbers and returns the midrange, the working written out with your real numbers, and the count, minimum, maximum, range, mean and median beside it. It updates as you type. Nothing you paste leaves your browser.
How to use the Midrange Calculator
The midrange is one line of arithmetic. It doesn't need an account, a trial that turns into a subscription, or a statistics package priced per seat. It needs a text box, so that's what you get.
- Paste or type your numbers into the box. Commas, spaces, semicolons, tabs and line breaks all work as separators, so a column copied straight out of a spreadsheet goes in as it is.
- Read the midrange at the top. There's no Calculate button. The answer changes as you type.
- Check the working line under it, for example
(6 + 20) ÷ 2 = 13. That's the line a homework question usually wants written down. - Look at the strip underneath: n, min, max, range, mean and median. If the midrange sits close to the mean and median, your data is balanced. If it's far away, one end of your list is doing something odd.
- Copy what you need. One button copies just the midrange. The other copies the whole summary on one line, like
n=7, min=6, max=20, range=14, midrange=13, mean=12.7142857142857, median=12.
If you paste a column with a header on top, like "Score", the page skips the word and tells you it skipped one entry. It never turns text into a zero, because a fake zero would quietly become your new minimum.
The midrange formula, worked through
Midrange = (minimum + maximum) ÷ 2
There are only two inputs:
- Minimum: the smallest value in the set. With negative numbers, that's the most negative one, so −12 is smaller than −3.
- Maximum: the largest value in the set.
Take the seven quiz scores from earlier: 14, 9, 17, 11, 6, 20, 12.
- Find the minimum. Scan the list: 6.
- Find the maximum: 20.
- Add them: 6 + 20 = 26.
- Halve it: 26 ÷ 2 = 13.
The midrange is 13. You never needed to sort the list, and the other five scores played no part at all.
Now compare. The mean adds all seven scores (89) and divides by seven, which gives 12.7142857142857. The median sorts the list (6, 9, 11, 12, 14, 17, 20) and takes the middle value, 12. Three centres, three slightly different answers, all close together. That closeness tells you something: nothing unusual is hiding at either end of these scores.
The range is the other number built from the same pair: 20 − 6 = 14. Range measures spread and midrange measures centre. Put together, they say "this data runs 7 either side of 13".
A small detail that matters at the edges: the calculator works out half the minimum plus half the maximum, instead of adding first. The answer is the same for any normal data. But adding two numbers near the largest value a computer can store overflows to infinity, and a plain (MIN + MAX) / 2 formula falls over there. Halving first never does.
Midrange, mean and median on common data sets
The fastest way to understand the midrange is to watch it next to the other two centres. Every row below came out of the Midrange Calculator.
| Data set | Values | Midrange | Mean | Median |
|---|---|---|---|---|
| Evenly spaced | 10, 20, 30, 40, 50 | 30 | 30 | 30 |
| A week of daily highs (°F) | 64, 67, 70, 71, 73, 75, 79 | 71.5 | 71.2857142857143 | 71 |
| Test scores | 72, 85, 88, 90, 95 | 83.5 | 86 | 88 |
| Commute minutes, one bad day | 22, 24, 25, 23, 61 | 41.5 | 31 | 24 |
| One very low value | 1, 40, 42, 45, 47 | 24 | 35 | 42 |
| Winter lows (°C) | −12, −5, −3, 0, 4 | −4 | −3.2 | −3 |
Look at the first two rows. When data is evenly spread, all three centres land in the same place or within half a degree of each other. That's the case where the midrange earns its keep: you get a good-enough centre from two numbers.
Now look at the commute. Four normal days between 22 and 25 minutes, then one 61-minute day stuck behind a crash. The median shrugs it off at 24. The mean climbs to 31. The midrange jumps to 41.5, a commute you never actually had. Half of that one bad day's extra time went straight into the answer.
The "one very low value" row is the same effect in reverse. A single 1 in a list of forties pulls the midrange down to 24 while the median holds at 42. That's the tell. When the midrange drifts far from the median, don't report it as "the typical value". Go and look at the ends of your list first.
Where the midrange misleads, and what the calculator won't do
The midrange is honest about exactly two numbers. Here's where that bites:
- Outliers. One typo, like 610 instead of 61 in the commute list, moves the midrange from 41.5 to 316. The mean goes to 140.8 and the median stays at 24. If the strip shows the midrange far from the other two, check your extremes before trusting any of them.
- Skewed data. Incomes, house prices and response times have long tails. The midrange of a skewed set describes the gap between the extremes, not what a typical value looks like.
- Decimal commas. Commas separate values here, so
1,5is read as 1 and 5, with a midrange of 3. Use a full stop for decimals. - Grouped data. The calculator takes raw values, not class intervals like "10–19: 4 students". Type the actual values, or at least the smallest and largest ones.
What the Midrange Calculator does handle: negative numbers, decimals, a single value (its midrange is itself, range 0), and up to a million values at once. Decimal answers come out clean, so 0.1 and 0.2 give a midrange of 0.15, not the 0.15000000000000002 that raw floating-point math produces. Very large and very small results switch to a short form like 1.35e+308 so they fit on a phone screen.
If your numbers aren't coming out the way your textbook says, try this first: paste the list one value per line and check the n count. If n is lower than the number of values you meant to enter, something got skipped. The notice under the box will say how many.
Related calculations
The midrange is one centre among several. The Midrange Calculator already shows the mean and median beside it, and the tools below answer the questions it can't.
The median calculator gives you the centre that ignores outliers entirely, which is the one to report when your midrange and median disagree. The average calculator covers the mean and mode, the centres that use every value.
For spread, the interquartile range calculator measures the middle 50% of your data, so a single extreme can't distort it the way it distorts the range. The standard deviation calculator tells you how far values typically sit from the mean.
And if you only have two numbers, or two points on a graph with x and y coordinates, the midpoint calculator is built for that.
Frequently asked questions
Can the midrange be a number that isn't in my data?
Yes, and it usually is. The midrange of 3, 7, 8, 12 and 20 is 11.5, and no one in that list scored 11.5. It's a halfway point between two values, not one of the values. The mode, and the median of an odd-length list, are the centres guaranteed to be actual data points.
Can the midrange be negative?
Yes, whenever the minimum is further below zero than the maximum is above it. For −8, −2 and 5, the midrange is (−8 + 5) ÷ 2 = −1.5. The winter lows of −12, −5, −3, 0 and 4 give −4. Negatives need no special handling. Paste them with an ordinary minus sign, or the typographic one a textbook PDF uses. Both work.
Does the order of the numbers matter?
No. The midrange depends only on which value is smallest and which is largest, and those don't change when you shuffle the list. Typing 20, 6, 12 gives the same midrange of 13 as 6, 12, 20. You don't need to sort anything before you paste.
If I add a value in the middle, does the midrange change?
Not unless the new value is below the current minimum or above the current maximum. Add 13 to the quiz scores 14, 9, 17, 11, 6, 20, 12 and the midrange stays at 13. The mean moves from 12.7142857142857 to 12.75, and the median moves from 12 to 12.5. That's the midrange's blind spot in one example.
How do I find the midrange from a frequency table?
Ignore the frequencies. The midrange only needs the smallest and largest values that actually appear, meaning any value with a count of at least one. If a table lists scores 4 through 10 but nobody scored 4, the minimum is 5. Type those two values into the calculator, or type all the raw values if you also want the mean and median.
How do I calculate the midrange in a spreadsheet?
Mainstream spreadsheet apps don't have a MIDRANGE function, so you write it yourself: =(MIN(A2:A50)+MAX(A2:A50))/2. That works for ordinary data. If you want to check it, paste the same column here. You'll see the working line, and the mean and median beside it, so you can tell whether the number your formula returned is a fair centre or just the gap between two extremes.
What does "midrange" mean on a salary band?
In HR, a pay band's midrange (often called the range midpoint) is halfway between the band's minimum and maximum salary. It's the same arithmetic on two numbers. A band of $60,000 to $80,000 has a midrange of $70,000. This page is built for statistics on a full data set, but typing the two ends of a band gives you the same answer.