Calculate the mean, median, mode, and range of any number set. See the sorted data, minimum, maximum, sum, count, frequency, and step-by-step math behind every answer.
Enter your values below and click Calculate for instant results.
Separate numbers with commas, spaces, or one number per line. Positive numbers, negative numbers, whole numbers, decimals, duplicates, and zero are all accepted. Example: 5, 3, 8, 5, 12, 3, 5, 9, 1
Mean, median, mode, and range are four ways to describe a set of data, but they do not all tell you the same thing.
The mean describes an arithmetic average. The median finds the middle of the ordered data. The mode identifies the value that occurs most often. The range measures the distance between the smallest and largest values.
Consider the data: 5, 3, 8, 5, 12, 3, 5, 9, 1. Sort the values: 1, 3, 3, 5, 5, 5, 8, 9, 12. The mean is approximately 5.67. The median is 5. The mode is 5. The range is 11. These four results describe different features of the same data set.
The mean is found by adding every value and dividing the total by the number of values. Formula: Mean = Sum of Values / Number of Values.
Using 5, 3, 8, 5, 12, 3, 5, 9, 1, first find the sum: 5+3+8+5+12+3+5+9+1 = 51. There are 9 numbers. Therefore Mean = 51/9 = 5.666... Rounded to two decimal places: 5.67.
In everyday school math, the word average usually refers to the arithmetic mean.
Every observation contributes to the total used in the mean. Consider 2, 4, 6. Mean: (2+4+6)/3 = 4. If 6 changes to 60, the data becomes 2, 4, 60. Mean: 66/3 = 22. A single extreme value can therefore move the mean dramatically.
This sensitivity can be useful because the mean reflects every observation, but it can also make the mean less representative of a typical value in heavily skewed data.
The median is the middle value after the data has been sorted from smallest to largest. Example: 9, 3, 7, 1, 5. First sort: 1, 3, 5, 7, 9. There are 5 values. The middle value is 5. Therefore Median = 5.
When the data contains an even number of observations, there is no single middle value. Use the two middle values and find their mean. Example: 2, 4, 7, 10. The middle numbers are 4 and 7. Calculate: (4+7)/2 = 11/2 = 5.5. Therefore Median = 5.5.
The median depends on position. Without sorting, the number physically written in the middle of the input may have no statistical meaning. Consider 100, 2, 5, 3, 4. The third value as written is 5. But first sort: 2, 3, 4, 5, 100. Now the actual median is 4. Always sort before finding the median.
This calculator does that automatically and shows the sorted data so you can see exactly where the median came from.
The mode is the value that occurs most frequently. Example: 2, 3, 3, 5, 7. Counts: 2 appears once. 3 appears twice. 5 appears once. 7 appears once. The most frequent value is 3. Therefore Mode = 3.
Yes. Example: 1, 1, 2, 2, 3. The number 1 appears 2 times. The number 2 also appears 2 times. No other number appears as frequently. Therefore the data has two modes: 1 and 2. This is called bimodal.
A data set can also have more than two values tied for the highest frequency. This calculator displays every tied mode rather than arbitrarily choosing only one.
Yes. Consider 1, 2, 3, 4, 5. Every value occurs exactly once. No value occurs more frequently than another. Therefore the set has no mode.
This calculator displays No Mode instead of incorrectly listing every value as a mode.
The range measures the distance between the largest and smallest values. Formula: Range = Maximum - Minimum.
Example: 1, 3, 3, 5, 5, 5, 8, 9, 12. Minimum: 1. Maximum: 12. Range: 12-1 = 11.
Range gives a quick idea of how far the data stretches from its lowest value to its highest value. Compare Data Set A: 48, 49, 50, 51, 52. Range: 52-48 = 4. Data Set B: 20, 35, 50, 65, 80. Range: 80-20 = 60. Both sets have a mean of 50. But their spreads are very different. Range makes that difference immediately visible.
However, range uses only minimum and maximum. It ignores how the values between those endpoints are distributed. For a more detailed measure of spread, the Standard Deviation Calculator can examine how values vary around the mean.
Mean and median both describe the center of numerical data, but they respond differently to extreme values. Consider 10, 11, 11, 12, 13. Mean: 11.4. Median: 11.
Now replace 13 with 100. The data becomes 10, 11, 11, 12, 100. Mean: 28.8. Median: 11. The extreme value 100 pulls the mean upward. The median remains 11 because the middle position has not changed.
The mean is often useful when the data is numerical, all observations should influence the result, the distribution is not dominated by extreme outliers, and you want an arithmetic average.
Example: Quiz scores: 82, 84, 86, 88, 90. Sum: 430. Count: 5. Mean: 86. Because the scores are fairly balanced, the mean provides a useful summary of the center.
The median can be more useful when numerical data is strongly skewed or contains extreme values. Consider home prices: $220,000, $240,000, $260,000, $280,000, $2,500,000. Median: $260,000. The very expensive home raises the mean dramatically. The median better identifies the middle transaction in this specific data set.
That does not mean the median is always better. The correct measure depends on what you want to understand.
The mode is useful when the most common value matters. Example: Shoe sizes sold: 8, 9, 9, 9, 10, 10, 11. Mode: 9. A store might find the mode useful when estimating which size is purchased most often.
Mode is also unusual among common measures of center because the idea can apply to categorical data. Example: shirt colors: Blue, Black, Blue, White, Blue. Mode: Blue. The calculator itself remains designed for numerical lists, but the mathematical concept of mode extends beyond numbers.
Range is useful when you want a simple answer to "How far apart are the smallest and largest values?" Example: Daily temperatures: 61, 64, 67, 71, 75. Range: 75-61 = 14 degrees.
Range is simple and intuitive. But because it depends entirely on the minimum and maximum, one extreme value can change it dramatically.
Outliers do not affect every measure equally. Consider 5, 6, 6, 7, 8. Mean: 6.4. Median: 6. Mode: 6. Range: 3.
Now add 100. Data: 5, 6, 6, 7, 8, 100. The mean increases substantially. The median changes because the number of values changes and the central positions change. The mode remains 6. The range jumps dramatically because the new maximum is 100.
This is why looking at more than one descriptive statistic can reveal more than using a single value.
Median describes position after sorting. Mode describes frequency. Example: 1, 2, 2, 3, 100. Median: 2. Mode: 2. Here they happen to match.
But consider 1, 2, 3, 4, 4. Median: 3. Mode: 4. There is no rule requiring the median and mode to be the same.
Median describes center. Range describes spread. Example: 10, 20, 30. Median: 20. Range: 20. These numbers may happen to match numerically, but they represent completely different characteristics of the data.
The mean uses arithmetic. The mode uses frequency. Example: 2, 2, 2, 10. Mode: 2. Mean: 4. The most common number and the arithmetic average are not necessarily the same.
Yes. Example: 1, 2, 2, 2, 3. Mean: 2. Median: 2. Mode: 2. All three measures of center are 2. That does not happen for every data set.
Example: 7. Mean: 7. Median: 7. Mode: there is usually no mode under this page's definition because the only value occurs once and there is no repeated most-frequent value. Range: 7-7 = 0. This calculator stays consistent with its mode convention in every case, including a single value.
Yes. Example: 1.5, 2.5, 2.5, 3.5. Mean: 2.5. Median: 2.5. Mode: 2.5. Range: 3.5-1.5 = 2.
Yes. Example: -5, -3, -3, 1, 5. Mean: -1. Median: -3. Mode: -3. Range: 5-(-5) = 10. The subtraction of a negative minimum is important when finding the range.
In most everyday arithmetic questions, average means arithmetic mean. To find it, add all values and divide by how many values there are.
However, statistics contains several ways to describe a typical or central value. That is why this page distinguishes mean, median, and mode instead of calling all three simply averages.
Central tendency refers to methods used to describe the center or typical location of a data set. The most familiar measures are mean, median, and mode.
Range is not a measure of central tendency. Range is a simple measure of variability or spread. This distinction matters: do not call range a measure of central tendency.
Use 5, 3, 8, 5, 12, 3, 5, 9, 1.
A useful check is: Mean × Count = Sum, allowing for rounding. Example: Mean: 5.666... Count: 9. 5.666...×9 = 51. That matches the sum.
If using a rounded mean such as 5.67, the multiplication will be close but may not equal exactly 51 because the displayed mean was rounded.
Sorted data makes several calculations easier to understand. You can immediately see minimum, maximum, middle position, repeated values, and range endpoints.
A calculator that only prints Mean = 5.67, Median = 5, Mode = 5, Range = 11 gives answers. Showing the sorted data helps show why those answers are correct.
Count is the number of observations entered. It is often written n. Example: 5, 3, 8, 5, 12, 3, 5, 9, 1 contains 9 observations. Therefore n=9. The count is required when calculating the mean.
The sum is the total of every value. It can be written using sigma notation: Σx. For 5, 3, 8, 5, 12, 3, 5, 9, 1 the sum is 51. Mean: Sum / Count = 51/9.
Range measures only the distance from minimum to maximum. Standard deviation considers how observations vary around the mean. Two data sets can have the same range but very different internal distributions.
If you need a fuller measure of spread, use the Standard Deviation Calculator.
Use this Mean, Median, Mode and Range Calculator when your primary question is about those four basic measures.
Use the Statistics Calculator when you need a broader descriptive statistical summary, such as quartiles, IQR, additional descriptive statistics, or a wider statistical summary. This page keeps the tools distinct instead of duplicating every Statistics Calculator feature here.
Keep enough precision during the calculation and round the final mean according to the instructions for your problem. Example: 17÷3 = 5.666666... If asked for two decimal places, report 5.67. If asked for one decimal place, report 5.7.
Use the Rounding Calculator for detailed rounding rules.
Mean, median, mode, and range are commonly taught together because each highlights a different feature of a data set. If you want an additional interactive lesson after working through the examples here, IXL also provides a mean, median, mode, and range lesson for extra practice.
Forgetting to sort before finding the median. Median requires ordered data.
Dividing the mean by the wrong count. Divide the sum by the number of observations.
Assuming there must always be a mode. Some data sets have no mode.
Returning only one mode when values tie. A data set can have multiple modes.
Calculating range backwards. Use Maximum - Minimum.
Forgetting that the minimum can be negative. Example: 5 - (-8) = 13.
Thinking range is an average. Range measures spread. It is not a measure of center.
Assuming median is always better than mean. The best measure depends on the data and the purpose.
Ignoring outliers. Outliers can substantially change mean and range.
Rounding the mean too early. Keep greater precision during the calculation.
Do not leave knowing only four numbers. Leave knowing:
And most importantly: I can see how each result was calculated from my data. That is what the CalculateThisWay Mean, Median, Mode and Range Calculator should help someone understand.
| Measure | Formula / Rule | What It Describes |
|---|---|---|
| Mean | Sum ÷ Count | Arithmetic average |
| Median | Middle ordered value | Center by position |
| Even Median | Average of two middle values | Center by position |
| Mode | Most frequent value(s) | Frequency |
| Range | Maximum - Minimum | Overall spread |
| Minimum | Smallest value | Lower endpoint |
| Maximum | Largest value | Upper endpoint |
| Count | Number of observations | Data set size |
| Sum | Total of all values | Used to calculate mean |
I need the basic center and range of a list of numbers.
You are hereI need a broader descriptive summary such as quartiles, IQR, or additional statistical measures.
Open Calculator ›I need to measure how spread out values are around the mean.
Open Calculator ›I already calculated a mean or another statistic and need to round it properly.
Open Calculator ›I need to calculate the likelihood of an event instead of summarizing a data set.
Open Calculator ›What is mean?
Mean is the arithmetic average of a set of numbers, found by adding every value together and dividing by how many values there are.
What is mean in math?
In math, the mean is the sum of a data set divided by the number of values in that data set. For 5, 3, 8, 5, 12, 3, 5, 9, 1 the sum is 51, the count is 9, so the mean is 51 divided by 9, about 5.67.
What is the mean definition in math?
Mean = Sum of Values / Number of Values. It is the arithmetic average and the most common meaning of the everyday word average.
How do you find the mean?
Add every value to get the sum, count how many values there are, then divide the sum by the count. 51 divided by 9 is approximately 5.67.
Is mean the same as average?
In everyday school math, yes. The word average almost always refers to the arithmetic mean, which is what this calculator reports as Mean.
What is median?
The median is the middle value in a data set after the values have been sorted from smallest to largest.
What is median in math?
Median is a measure of center found by position rather than arithmetic. For 1, 3, 5, 7, 9 the median is 5, the middle value.
How do you find the median?
Sort the values from smallest to largest. If there is an odd number of values, the median is the middle one. If there is an even number, average the two middle values.
Do you have to sort numbers to find the median?
Yes. The median depends entirely on position in sorted order. For 100, 2, 5, 3, 4, sorting gives 2, 3, 4, 5, 100, and the median is 4, not the unsorted middle value.
How do you find median with an even number of values?
Sort the data, take the two middle values, and find their mean. For 2, 4, 7, 10 the middle values are 4 and 7, and (4+7)/2 = 5.5.
What is mode?
The mode is the value, or values, that occur most often in a data set.
What is mode in math?
Mode is the measure of center based on frequency rather than arithmetic or position. For 2, 3, 3, 5, 7 the mode is 3 because it appears twice.
How do you find the mode?
Count how many times each value appears. The value, or values, with the highest frequency is the mode. If every value appears the same number of times, there is no mode.
Can there be two modes?
Yes. This is called bimodal. For 1, 1, 2, 2, 3 both 1 and 2 appear twice, more than any other value, so the data has two modes: 1 and 2.
Can there be more than two modes?
Yes. When three or more values are tied for the highest frequency, the data set has multiple modes, and this calculator lists every tied value.
Can there be no mode?
Yes. If every value in the data set occurs exactly once, no value occurs more frequently than another, so the calculator reports No Mode instead of listing every value.
What is range?
Range is the distance between the largest and smallest values in a data set, calculated as Maximum minus Minimum.
What is range in math?
Range measures spread, not center. For 1, 3, 3, 5, 5, 5, 8, 9, 12, the range is 12 minus 1, which equals 11.
What is the range meaning in maths?
In maths, range describes how far data values stretch from the lowest value to the highest value. It is a simple measure of variability.
How do you find range?
Identify the maximum value and the minimum value in the data set, then subtract the minimum from the maximum.
Is range maximum minus minimum?
Yes. Range = Maximum - Minimum. For example, with a minimum of -8 and a maximum of 5, the range is 5 - (-8) = 13.
What is mean median mode and range?
They are four different ways to describe a data set: mean is the arithmetic average, median is the middle value after sorting, mode is the most frequent value, and range is the distance between the maximum and minimum.
What is the difference between mean median mode and range?
Mean, median, and mode are measures of central tendency that describe the center of the data in different ways. Range is a measure of spread, not center, and only depends on the two extreme values.
Which is better, mean or median?
Neither is always better. The mean uses every value and works well for balanced data. The median is usually more resistant to outliers and can better represent skewed data such as home prices.
When should I use mean?
Use the mean when the data is numerical, every observation should count, and the distribution is not dominated by extreme outliers.
When should I use median?
Use the median when the data is skewed or contains extreme values, such as a handful of very high or very low numbers that would distort the mean.
When should I use mode?
Use the mode when you want to know which value or category occurs most often, such as the most commonly sold shoe size.
When should I use range?
Use range for a quick, simple sense of how spread out a data set is from its lowest to its highest value.
How do outliers affect the mean?
Outliers can move the mean substantially because the mean uses every value. Changing 13 to 100 in 10, 11, 11, 12, 13 moves the mean from 11.4 to 28.8.
How do outliers affect the median?
The median is usually much more resistant to outliers because it depends on position, not magnitude. In the same example, the median stays at 11 even after the outlier is introduced.
How do outliers affect the range?
Range can change dramatically from a single outlier because it depends only on the minimum and maximum values.
Can mean median and mode be the same?
Yes. For 1, 2, 2, 2, 3 the mean, median, and mode are all 2, though this does not happen for every data set.
What happens if there is only one number?
With a single value such as 7, the mean is 7, the median is 7, the range is 0, and there is no mode because the one value only occurs once.
Can mean median mode and range use negative numbers?
Yes. For -5, -3, -3, 1, 5 the mean is -1, the median is -3, the mode is -3, and the range is 5 minus -5, which equals 10.
Can they use decimals?
Yes. For 1.5, 2.5, 2.5, 3.5 the mean, median, and mode are each 2.5, and the range is 3.5 minus 1.5, which equals 2.
What is central tendency?
Central tendency refers to methods for describing the center or typical location of a data set. The most familiar measures are mean, median, and mode.
Is range a measure of central tendency?
No. Range is a measure of spread, or variability, not central tendency. It describes how far the data stretches, not where its center is.
What is the difference between range and standard deviation?
Range only considers the minimum and maximum values. Standard deviation considers how every value varies around the mean, so it is a more detailed measure of spread.
How do I round the mean?
Keep extra precision during the calculation, then round the final result to the number of decimal places your problem requires. 17 divided by 3 is 5.666..., which rounds to 5.67 at two decimal places.
Last reviewed: October 1, 2026