Mean, Median and Mode Calculator
The mean, median and every mode of a data set, with its range and quartiles.
Result
Mean: 5
Exact arithmetic on the values entered. Nothing is estimated.
- Median
- 4.5
- Mode
- 4
- Range
- 7
- Smallest value
- 2
- Largest value
- 9
- First quartile, Q1
- 4
- Third quartile, Q3
- 5.5
- Interquartile range
- 1.5
- Midrange
- 5.5
- Sum
- 40
- Count
- 8
https://calcgallery.com/statistics/mean-median-mode-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Mean, Median and Mode Calculator
- Enter your numbers, one per row. Add rows as you need them; a row you add and leave empty is ignored.
- Read the mean, then the median, the mode and the measures of spread below it.
The three averages
| Measure | How it is found | What it tells you |
|---|---|---|
| Mean | add every value and divide by how many there are | the balance point of the data |
| Median | sort the values and take the middle one, or the mean of the middle two | the value half the data sits below |
| Mode | the value or values that occur most often | the most common value, if one exists |
The mean uses every value, so a single extreme value moves it. The median ignores how far out the extremes are, only which side of the middle they fall. The mode is the only one of the three that works for categories as well as numbers, and it is the only one that can be missing or plural.
Spread
- Range is the largest value minus the smallest. It uses only two values, so a single outlier sets it.
- Quartiles split the sorted data into four parts. Q1 has a quarter of the data below it, Q3 three quarters.
- Interquartile range, Q3 − Q1, is the spread of the middle half. It ignores the extremes, which makes it the usual companion to the median.
- Midrange is halfway between the smallest and largest values. It is rarely useful on its own, but it is easy to check.
For the spread around the mean, use the variance or standard deviation calculators.
Entering data
Enter numbers one per row. Negative numbers and decimals are fine. The page sorts a copy of your data to find the median and quartiles, so your rows stay in the order you typed them.
With your numbers
- Mean = sum ÷ count = 40 ÷ 8 = 5
- Median = the middle of the sorted values = 4.5
- Range = 9 − 2 = 7
Quick reference
Exact arithmetic on the values entered. Nothing is estimated.
| Example | Mean |
|---|---|
| 2, 4, 4, 4, 5, 5, 7, 9 | 5 |
| 1, 2, 3, 4 (no mode) | 2.5 |
| 1, 1, 2, 2, 3 (bimodal) | 1.8 |
| −3, −1, 0, 1, 3 | 0 |
| Test scores 72, 85, 90, 85, 68 | 80 |
| 3, 7, 7, 2, 9, 7, 3 | 5.428571 |
Common questions about the Mean, Median and Mode Calculator
- Which should I use, the mean or the median?
- The median when the data are skewed or have outliers, the mean when they are roughly symmetric. House prices and incomes are the classic skewed cases: a few very large values pull the mean up while the median stays with the typical value. When the two are far apart, that gap is itself worth reporting.
- What if no number repeats?
- Then the data set has no mode, and the page says so. Some calculators report the smallest value or every value instead, which is wrong: the mode is the most frequent value, and when every value occurs once there is no most frequent value.
- Can a data set have more than one mode?
- Yes. If two values tie for most frequent the set is bimodal, and with three or more it is multimodal. The page lists every one. Two clear modes often mean two different groups have been mixed together, such as the heights of adults and children.
- How are the quartiles worked out?
- By linear interpolation between the sorted values, the method spreadsheets use for PERCENTILE.INC and QUARTILE.INC (Hyndman and Fan type 7). Textbooks sometimes teach the median of each half instead, which can give a different Q3: for 2, 4, 4, 4, 5, 5, 7, 9 it gives 6 rather than 5.5. Both are legitimate conventions; this page uses one and names it.