Midrange Calculator

What the midrange calculator does

The midrange is the point exactly halfway between the smallest and largest values in your data. This calculator finds it, and shows you the minimum and maximum it used to get there.

It is the quickest measure of the centre there is, since it only needs the two ends. That makes it handy for a fast rough check, and it is the natural midpoint for something like a day's temperature, halfway between the high and the low. Below is how it works and the one thing to keep in mind about it.

How to use it

1. Enter your numbers in the box, separated by commas, spaces, or new lines.
2. Press Calculate to see the midrange along with the smallest and largest values, or Reset to clear it.

How the midrange is worked out

It is the simplest formula of all the averages. Find the smallest value, find the largest, and take the point halfway between them:

Midrange = (smallest value + largest value) ÷ 2

Everything in between is ignored. The calculator does not care whether you have five numbers or five hundred, only what the two ends are, which is exactly why it is so quick to work out.

The one thing to watch: it lives on the extremes

Because the midrange is built entirely from the two most extreme values, it is the most sensitive of all the averages to an outlier. A single unusually high or low number is not just included, it is one of the only two numbers that count. One freak value can swing the midrange a long way from where the bulk of your data actually sits.

So the midrange is at its best when the extremes are stable, or when the ends are the very thing you care about. When your data has a stray outlier and you want a figure that represents the typical value, the median is the safer choice, and the mean sits somewhere in between.

A worked example, and a wobble

Take the numbers 6, 9, 11, 14, 20. The smallest is 6 and the largest is 20, so the midrange is (6 + 20) ÷ 2 = 13. That sits nicely in the middle of this tidy set.

Now change that 20 to 200 and leave everything else alone. The midrange leaps to (6 + 200) ÷ 2 = 103, even though only one value moved and four of the five numbers are still down between 6 and 14. That is the midrange showing its nature: it is only ever as steady as its two extremes.

Entering your data, and the rounding

You can separate your numbers with commas, spaces, or new lines, in any mix, and the order does not matter, since the calculator only needs to find the smallest and largest. The midrange is shown to four decimal places with trailing zeros trimmed, which only shows up when the two ends do not average to a whole number.

Questions people ask

What is the midrange?

The value halfway between the smallest and largest numbers in a data set, found by adding the two and dividing by two. It is a quick measure of the centre.

How is the midrange different from the median?

The median is the middle value once the data is sorted, so it ignores the extremes. The midrange is built only from the extremes. That makes the median steady against outliers and the midrange very sensitive to them.

When is the midrange useful?

For a fast rough estimate of the centre, or when the two ends are what matter, like the midpoint between a daily high and low temperature. For a typical-value figure on messy data, prefer the median.

Why did one number change my midrange so much?

Because the midrange uses only the smallest and largest values. If your new number becomes a new extreme, it directly moves the result, no matter how the rest of the data looks.

References

A quick note on where the methods here come from. The midrange and the other measures of the centre of a data set are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers measures of centre and how outliers affect them.

1. NIST/SEMATECH e-Handbook of Statistical Methods (measures of location). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (measures of the center of the data). https://openstax.org/details/books/introductory-statistics-2e