What is the Mean, Median, Mode, Range Calculator?
The statistical concepts of mean, median, mode, and range serve as fundamental blocks in analyzing and understanding sets of data. Depending on the context, mathematical or statistical, what is "typical" or "expected" can change. In general, mean, median, mode, and range should ideally all be computed and analyzed for a given sample or data set since they elucidate different aspects of the given data. If considered alone, one metric might lead to a misrepresentation of the data.
Use this calculator to quickly deduce central tendency metrics from raw lists of numerical data.
How to Use This Calculator
To use the calculator, simply enter your sequence of numbers into the Data Set field. Make sure the numbers are separated by commas (e.g., 10, 2, 38, 23, 38, 23, 21). The calculator will instantly format your numbers, remove invalid characters, and compute all relevant statistics without needing to sort the numbers manually.
The Formula & The Methods
Mean (Average)
In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values.
Example: For data set 10, 2, 38, 23, 38, 23, 21
Mean = (10 + 2 + 38 + 23 + 38 + 23 + 21) / 7 = 155 / 7 = 22.143
The mean is often denoted as x̄, pronounced "x bar". In the specific case of the population mean, the Greek symbol mu, or μ, is used.
Median
The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers when they are ordered.
Rule (Even amount of numbers): The median is the average (mean) of the two middle numbers.
Example (Sorted): 2, 10, 21, 23, 23, 38, 38. The middle is 23.
Note that in a data set with extreme outliers, the median is often a far better representation of a "typical value" than the mean.
Mode
In statistics, the mode is the value in a data set that has the highest number of recurrences. It is possible for a data set to be multimodal, meaning that it has more than one mode.
Both 23 and 38 appear twice each, making them both a mode for the data set above.
Unlike mean and median, the mode is a concept that can be applied to non-numerical values (e.g., the most commonly purchased brand of chips).
Range
The range of a data set in statistics is the difference between the largest and the smallest values. It provides a simple indication of statistical dispersion.
Example: For max 38 and min 2, Range = 38 - 2 = 36.
Frequently Asked Questions
The mean is the mathematical average of a set of numbers, found by adding them all together and dividing by the total count. The median is the physical middle value when the numbers are sorted from smallest to largest. The mean can be skewed by extremely high or low values (outliers), whereas the median provides a more accurate central point in skewed data sets.
Yes. A data set is said to be "bimodal" if it has two modes, and "multimodal" if it has more than two. If every number in a dataset appears an equal number of times, it is typically said that the dataset has no mode.
Outliers (extremely large or small values) have a heavy impact on the mean and the range, skewing the results toward the outlier. However, outliers typically have little to no effect on the median and the mode, making those two metrics much more robust against anomalous data.
You should use the median instead of the mean when your data set has a skewed distribution or contains outliers. A classic example is household income: a few billionaires can skew the mean income very high, so median income gives a much better picture of what the "typical" household earns.
The range gives you a basic measure of the spread or dispersion of your data. A larger range indicates that the data points are spread out over a wider array of values, while a smaller range indicates that the data points are clustered closely together.