Midrange formula
The midrange is the value exactly halfway between the smallest and the largest number in a data set. Add the minimum and the maximum, then divide by two:
Midrange = (Minimum + Maximum) ÷ 2 How to find the midrange of a data set
Take the data set 12, 15, 18, 22, 30:
- Find the smallest value. Here the minimum is 12.
- Find the largest value. Here the maximum is 30.
- Add them together: 12 + 30 = 42.
- Divide by 2: 42 ÷ 2 = 21.
So the midrange is 21. Notice that 21 isn't one of the numbers in the set, and it doesn't have to be — the midrange is a midpoint, not a member of the data.
Sorting the data first isn't strictly necessary, since you only need the two extremes, but it makes them easier to spot on a long list. Every value between the smallest and largest is ignored entirely by this calculation.
Why the Midrange Can Be Misleading
Because the midrange uses only two numbers, it's the fastest measure of centre to work out by hand — no sorting through the middle of the list, no adding everything up. That speed is also its weakness. Those two numbers are the most extreme values in the set, which makes the midrange the measure most easily thrown off by a single unusual reading.
The midrange is not the median, and not the mean
These three are often confused because all three are described as measures of "centre" or "average". They're calculated from different information and usually give different answers:
- Midrange uses only the lowest and highest value. Every other number in the set has no effect on it at all.
- Median is the middle value once the data is in order. It ignores how far away the extremes are — only their position in the order matters.
- Mean (the everyday "average") adds every value and divides by how many there are, so every number contributes.
For the same data set 12, 15, 18, 22, 30, all three differ:
- Midrange: (12 + 30) ÷ 2 = 21
- Median: the middle value in order = 18
- Mean: 97 ÷ 5 = 19.4
The gap widens sharply when a data set contains an outlier. For 1, 2, 3, 4, 100 the midrange is 50.5 — higher than every value in the set except one — while the median is just 3. The single value of 100 drags the midrange up on its own, because it happens to be one of the two numbers the formula looks at. The median barely moves, because it only cares that 100 sits at the end of the order, not how far out it is.
When is the midrange useful?
It's genuinely useful when the extremes are the point. A daily temperature midrange — halfway between the day's low and high — is a standard weather figure, because the two extremes are what was actually recorded and what people care about. It's also a reasonable quick estimate of centre for small, clean data sets with no unusual readings, and it's a normal step in statistics coursework on measures of central tendency.
It's a poor choice for data with outliers, for skewed distributions, or for anything where a single bad measurement could slip in. In those cases, the median is usually more robust, and measures such as the interquartile range (IQR) are useful for describing spread without relying heavily on extreme values.
Frequently asked questions
What is the midrange formula?
Midrange = (Minimum + Maximum) ÷ 2. Add the smallest and largest values in the data set together, then divide that total by 2. No other value in the set affects the result.
Is the midrange the same as the median?
No. The median is the middle value once the data is sorted; the midrange is the midpoint between the two extremes. They coincide on perfectly symmetrical data and otherwise usually don't. For 12, 15, 18, 22, 30 the median is 18 while the midrange is 21.
Is the midrange the same as the range?
No, and the similar names cause a lot of mix-ups. The range is maximum minus minimum and measures how spread out the data is. The midrange is maximum plus minimum, divided by two, and estimates where the centre sits. For 12 to 30, the range is 18 and the midrange is 21.
Can the midrange be a number that isn't in my data set?
Yes, and usually it is. The midrange is a midpoint, so it only lands on an actual data value by coincidence. It can also fall outside the range where most of your values cluster, which is exactly what happens when one extreme sits far from the rest.
Can I use negative numbers or decimals?
Yes. The midrange is defined for any real numbers, so negatives and decimals both work normally, and the midrange itself can be negative or fractional. For −10, −2 and 8 the midrange is −1.