Three quick ways to describe a list
Median, mode and range are the first statistics most people learn, and they are handy every day. The median is the middle value, the mode is the most common one, and the range is the gap between the highest and the lowest. Together with the mean they give a fast picture of any list, from test scores to house prices.
This median, mode and range calculator sorts your numbers, points out the middle position, and shows every step, which makes it useful for checking homework as well as for real data.
How to use it
- Type or paste your numbers, separated by commas, spaces or new lines.
- Read the median first, then the mode, range, mean and midrange.
- Open the working to see the sorted list and which values sit in the middle.
- Use a point for decimals, such as 2.5, since commas separate the numbers.
How each one is found
median: sort the list; take the middle value, or the average of the two middle values
mode: the value that appears most often (there can be several, or none)
range = highest − lowest; midrange = (highest + lowest) ÷ 2
mean = sum ÷ countFor an odd count, the median is the value at position (n + 1) ÷ 2. For an even count, it is halfway between the values at positions n ÷ 2 and n ÷ 2 + 1.
Worked example: 7, 3, 9, 3, 5, 8
- Sorted: 3, 3, 5, 7, 8, 9
- Six values, so the middle two are the 3rd and 4th: (5 + 7) ÷ 2 = 6
- Mode: 3 (2 times)
- Range: 9 − 3 = 6; mean: 35 ÷ 6 = 5.8333
The median is 6, the mode is 3, the range is 6 and the mean is 5.8333. Here the median sits above the mean, because the two low 3s pull the average down.
When to use which
| Measure | Best for | Weak spot |
|---|---|---|
| Median | Lists with a few extreme values, such as pay or prices | Ignores how far the other values are |
| Mode | Repeated values and categories, such as sizes or ratings | May not exist, or there may be several |
| Mean | Balanced lists, and totals | Pulled hard by extreme values |
| Range | A quick sense of spread | Set by just two values |
If the range is driven by one odd value, the quartile and outlier calculator gives a sturdier measure of spread.
More statistics
- For standard deviation and variance as well, use the statistics calculator.
- For a plain or weighted mean, the average calculator is simplest.
- Order matters only for the median; the mode and range ignore it.
- Data with units, such as heights in cm, keeps those units: the median, mode and range are all in cm too.
Frequently asked questions
How do I find the median?
Sort the numbers from lowest to highest and take the one in the middle. With an even number of values, take the two in the middle and average them. For 3, 3, 5, 7, 8, 9, the middle two are 5 and 7, so the median is 6. The calculator shows these positions.
What if there are two modes or no mode?
If two values tie for appearing most often, both are modes, and the list is called bimodal. If every value appears only once, there is no mode. The calculator lists every mode, with how many times each appears, or says that no value repeats.
How do I find the range?
Subtract the lowest value from the highest. For a list running from 3 to 9, the range is 9 − 3 = 6. The range is quick to find, but because it depends only on those two values, one unusual number can make it look much larger.
What is the difference between mean and median?
The mean adds every value and divides by the count, so a very large or small value pulls it hard. The median is simply the middle value, so it hardly moves when one value is extreme. That is why incomes and house prices are often reported as medians.
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