Reference text
Calculator.net explanations
Everything from the original mean, median, mode, range calculator lives here so you can reference derivations and use the Pixalor UI simultaneously.
Mean
Mean, which is sometimes pronounced "x-bar," is the arithmetic average of a collection of values. In mathematical notation it is written as x̄ = (1/n) Σ xᵢ, where n is the number of values and xᵢ denotes each individual observation.
Using calculator.net's reference data set 10, 2, 38, 23, 38, 23, 21 the mean is computed as (10 + 2 + 38 + 23 + 38 + 23 + 21) / 7 = 22.142857. The same expression works for both population and sample data with the only difference being whether the denominator uses N or n.
Because every value contributes to the mean, it is sensitive to outliers or extremely skewed data. Understanding the definition and its sensitivity helps ensure correct interpretation and allows the mean to remain one of the most fundamental statistical summaries.
Median
The median is the value that divides a data set such that exactly half of the observations are below the median and half are above. To determine it, sort the values in ascending order and take the middle entry.
For the ordered sample 2, 10, 21, 23, 23, 38, 38 the median equals 23 because it is the fourth value in the seven-point list. If the sample had an even number of observations, the median would be the average of the two central values, ensuring that it still bisects the distribution.
Because the median focuses on the ordering of data rather than the magnitude of each number, it is far less affected by outliers and can be a more reliable representation of "typical" values when the data contains extreme highs or lows.
Mode
Mode refers to the value that occurs most frequently in the data set. If two or more values tie for the highest frequency, the data set is multi-modal. With the sample used here, both 23 and 38 appear twice, so the data is bimodal.
When every value appears exactly once, there is technically no mode. Conversely, when a single value dominates the frequency table it can provide an intuitive picture of the data's behavior, especially for categorical or discrete measurements.
Range
Range gives the simplest measure of spread by subtracting the smallest value from the largest. With the reference data set the range equals 38 - 2 = 36.
Range, like the mean, can be dramatically altered by extreme values. It is best used in conjunction with other statistics or when emphasizing how broadly the data values are distributed.