Mean Median Mode Calculator
For the ten numbers 4, 7, 2, 9, 7, 3, 7, 5, 9 and 1, the mean median mode calculator gives a mean of 5.4, a median of 6, a mode of 7 and a range of 8.
Mean (average)
- Mean (average) Sum of 54 divided by 10 values.
- 5.4
- Median Halfway between the two middle values once sorted, the 5th and 6th: (5 + 7) / 2.
- 6
- Sorted
- 1, 2, 3, 4, 5, 7, 7, 7, 9, 9
- Mode The value that appears most often: 3 times.
- 7
- Range From 1 to 9.
- 8
- Count
- 10
- Sum
- 54
- Geometric mean The nth root of the product. The right average for growth rates and ratios that compound.
- 4.49051
- Harmonic mean The count divided by the sum of reciprocals. The right average for speeds over equal distances.
- 3.40817
- The mean is below the median, pulled down by the low values.
How the Average Calculator works
The mean, the median and the mode are three ways to pick one number that is typical of a list, and the range says how spread out the list is. The formula for the mean, median and mode is a short rule each, worked through here on the list 4, 7, 2, 9, 7, 3, 7, 5, 9, 1.
Mean. Add the values and divide by how many there are. The formula is mean = Σx / n. For the default list the sum is 4 + 7 + 2 + 9 + 7 + 3 + 7 + 5 + 9 + 1 = 54 over 10 values, so the mean is 5.4. The mean need not be one of the values, and need not be a whole number.
Median. Sort the list and take the middle value. Sorted, the default list is 1, 2, 3, 4, 5, 7, 7, 7, 9, 9. With an even count there are two middle values, the 5th and the 6th, so the median is halfway between them: (5 + 7) / 2 = 6. With an odd count it is the single value in position (n + 1) / 2. Add a 10 to the list and there are 11 values, so the median is the 6th: 7.
Mode. The value that appears most often. In the default list 7 appears three times and nothing else more than twice, so the mode is 7. A list can have two modes (bimodal) or more: add another 9 and both 7 and 9 appear three times. A list where every value appears once has no mode, not a mode equal to every value.
Range. The largest value minus the smallest: 9 - 1 = 8. It is the simplest measure of spread, and it depends on just the two most extreme values.
Which one to use. For a roughly symmetric list the mean and median are close, as here (5.4 and 6). One extreme value moves them apart. Change the 9 in the fourth place to 90 and the mean jumps to 13.5 while the median stays at 6 and the mode at 7. That is why incomes and house prices are reported as medians. The mode is the only one that works for categories, such as the most common shoe size sold or the most popular answer to a survey question.
For quartiles and percentiles of the same list, use the percentile calculator, and for spread beyond the range, the standard deviation calculator.
Average Calculator FAQ
How do you find the mean, median and mode?
Mean: add the values and divide by the count. Median: sort them and take the middle one, or the average of the two middle ones. Mode: the value that appears most often. For 4, 7, 2, 9, 7, 3, 7, 5, 9, 1 they are 5.4, 6 and 7.
How do you find the median of an even number of values?
Average the two middle values once sorted. In 1, 2, 3, 4, 5, 7, 7, 7, 9, 9 the 5th and 6th values are 5 and 7, so the median is 6.
What if there is no mode or more than one?
If every value appears once, there is no mode. If two or more values tie for most frequent, each is a mode: the list is bimodal or multimodal, and the calculator lists all of them.
How do you find the range?
Subtract the smallest value from the largest. For the default list that is 9 - 1 = 8.