Mean Median Mode Range Calculator
Enter your numbers to find the mean, median, mode, and range together, with each step shown. The calculator sorts your data, counts frequencies, and shows exactly how every answer is reached.
Paste your numbers and this calculator returns the mean, median, mode, and range together, each with the working shown. Type a set like 73, 45, 67, 87, 98 and you get the average (74), the middle value (73), the most frequent number (none here, since every value appears once), and the spread (53). It sorts the data for you, builds a frequency table, and lays out every step so you can copy the method into your homework, not just the final number.
Below you will find the formulas, worked examples using the exact number sets people search for, and quick reference tables for mean, median, mode, and range.
What Are Mean, Median, Mode, and Range?
These four values describe a data set in four different ways. The mean is the average. The median is the middle value once numbers are lined up in order. The mode is the number that shows up most often. The range is the gap between the largest and smallest value. Together they tell you where the center of your data sits and how spread out it is.
Quick definitions:
- Mean = add every number, divide by how many there are.
- Median = the middle value after sorting (average the two middle ones if the count is even).
- Mode = the value that appears most often (there can be one, several, or none).
- Range = largest value minus smallest value.
| Measure | What it tells you | Formula | Best used when |
|---|---|---|---|
| Mean | The average value | Sum ÷ count | Data has no extreme outliers |
| Median | The middle value | Middle of sorted list | Data has outliers or is skewed |
| Mode | The most common value | Highest frequency | You care about the most typical result |
| Range | How spread out the data is | Max − Min | You want a quick sense of variation |
How Do You Find the Mean, Median, Mode, and Range?
Take the set 73, 45, 67, 87, 98 as an example. Sort it first: 45, 67, 73, 87, 98. Now work through each measure.
Mean
Add every value, then divide by 5.
45 + 67 + 73 + 87 + 98 = 370
370 ÷ 5 = 74
Mean = 74
Median
Five values sorted: 45, 67, 73, 87, 98. The middle position is the 3rd number.
Median = 73
Mode
Every number appears exactly once, so nothing repeats.
Mode = None
Range
Largest is 98, smallest is 45.
98 − 45 = 53
Range = 53
How to Calculate the Mean (Average)
The mean is the sum of all values divided by how many values there are. It is written as x̄ (x-bar) for a sample, or μ (mu) for a population.
Mean = Σx ÷ n
Here Σx is the total of all the numbers and n is how many numbers you have. Add them up, divide, done.
Worked Example: Mean of 4, 7, 9
Sum: 4 + 7 + 9 = 20. Count: 3 values. Mean = 20 ÷ 3 = 6.67.
Population Mean vs Sample Mean
The math is identical. The only difference is what your data represents. If your numbers are the entire group you care about, you have a population mean (μ). If they are a smaller sample pulled from a bigger group, you have a sample mean (x̄). Both use sum divided by count.
How to Find the Median (Middle Value)
The median is the middle number once your data is sorted from smallest to largest. It splits the data in half. Half the values sit below it, half above.
Odd Number of Values
When the count is odd, the median is the single value in the exact center. Its position is (n + 1) ÷ 2. For 45, 67, 73, 87, 98 the position is (5 + 1) ÷ 2 = 3, so the 3rd value, 73, is the median.
Even Number of Values (Median With Two Middle Numbers)
When the count is even there is no single middle, so you average the two central values. Take 2, 5, 7, 9. The middle two are 5 and 7. Median = (5 + 7) ÷ 2 = 6.
Why the median matters: it ignores extreme values. In the set 4, 5, 6, 7, 200, the mean is dragged up to 44.4 by that single 200, but the median stays at 6, which describes the typical value far better.
How to Find the Mode (Most Frequent Value)
The mode is the value that appears most often. Build a frequency count, then pick whatever shows up the most.
- One mode (unimodal): one value repeats most. In 2, 3, 3, 5, 8 the mode is 3.
- Several modes (multimodal): two or more values tie for the top count. That set is bimodal or multimodal.
- No mode: every value appears once, like 45, 67, 73, 87, 98. There is no mode.
Unlike the mean and median, the mode works for non-number data too, such as the most common shoe size sold or the most picked survey answer.
How to Find the Range (Spread of the Data)
The range is the simplest measure of spread. Subtract the smallest value from the largest.
Range = Maximum − Minimum
Worked Example: Find the Range of 73, 45, 67, 87, 98
Largest is 98, smallest is 45. Range = 98 − 45 = 53.
Because the range only looks at two numbers, one unusual value can blow it out. The set 4, 5, 6, 7, 200 has a range of 196 even though most values sit close together. When that happens, the interquartile range (Q3 − Q1) gives a fairer picture of the spread.
Worked Examples Using Common Homework Sets
These are the exact number sets students search for most. Each answer below is calculated the same way the tool above does it.
| Data Set | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 73, 45, 67, 87, 98 | 74 | 73 | None | 53 |
| 34, 57, 69, 89, 104 | 70.6 | 69 | None | 70 |
| 17, 17, 18, 25, 27 | 20.8 | 18 | 17 | 10 |
| 18, 23, 10, 39, 22, 17, 16, 15 | 20 | 17.5 | None | 29 |
| 20, 14, 29, 39, 33, 25, 19, 35 | 26.75 | 27 | None | 25 |
| 26, 19, 23, 39, 31, 34, 23, 25 | 27.5 | 25.5 | 23 | 20 |
| 42, 54, 74, 75, 47, 49, 49 | 55.71 | 49 | 49 | 33 |
| 81, 78, 74, 88, 73, 76, 93, 98, 78, 80 | 81.9 | 79 | 78 | 25 |
| 15, 19, 13, 20 | 16.75 | 17 | None | 7 |
| 7, 4, 4, 5, 1, 9 | 5 | 4.5 | 4 | 8 |
Example: Find the Range of 34, 57, 69, 89, 104
Sorted, the smallest is 34 and the largest is 104. Range = 104 − 34 = 70. Mean = 353 ÷ 5 = 70.6, median = 69, and no value repeats so there is no mode.
Example: Daily Temperature Set (Mon to Fri: 64, 60, 54, 60, 62)
Sum = 300, so mean = 300 ÷ 5 = 60. Sorted: 54, 60, 60, 62, 64, so the median is 60. The value 60 appears twice, making it the mode. Range = 64 − 54 = 10.
Mean vs Median vs Mode: Which One Should You Use?
They answer different questions, so the right one depends on your data.
| Situation | Best measure | Reason |
|---|---|---|
| Test scores with no extreme values | Mean | Uses every value fairly |
| House prices or salaries | Median | Not distorted by a few huge values |
| Most popular product size | Mode | Shows the most common choice |
| Comparing consistency of two sets | Range | Shows which set is more spread out |
A quick tell: if the mean sits well above the median, a few high values are pulling the average up (right-skewed data). If the mean sits below the median, low values are pulling it down (left-skewed). When they are close, the data is fairly balanced.
What Is the Midrange?
The midrange is another center measure some courses ask for. It is the average of the highest and lowest values: (Max + Min) ÷ 2. For 73, 45, 67, 87, 98 that is (98 + 45) ÷ 2 = 71.5. It is quick but sensitive to outliers since it only uses two numbers.
Common Mistakes to Avoid
- Forgetting to sort the numbers before finding the median. The median only works on ordered data.
- Assuming every data set has a mode. If nothing repeats, there is no mode.
- Dropping repeated values when counting. 4, 4, 7 has three values, not two.
- Confusing range with the mean of the range. Range is just max minus min, one subtraction.
- Averaging the wrong two numbers for an even-count median. Sort first, then pick the two true middle positions.
Frequently Asked Questions
How do you calculate mean, median, and mode?
Mean: add all the numbers and divide by how many there are. Median: sort the numbers and take the middle one, or average the two middle ones if the count is even. Mode: find the value that appears most often.
How do you find the median with an even set of numbers?
Sort the numbers, find the two in the exact middle, add them, and divide by 2. For 15, 19, 13, 20, sorted it is 13, 15, 19, 20. The middle two are 15 and 19, so the median is (15 + 19) ÷ 2 = 17.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, the set is multimodal. If no value repeats at all, the set has no mode.
What is the difference between range and mean?
The mean is the average of every value. The range only measures spread, the distance between the largest and smallest number. They describe two different things: center versus spread.
How do you find the range in math?
Subtract the smallest value from the largest. That single subtraction is the whole method. For 12, 4, 7, 19 the range is 19 − 4 = 15.
For deeper work on spread, the standard deviation calculator shows how far values sit from the mean on average, and the outlier calculator flags the extreme values that distort the mean and range.