Mean, Median and Mode Calculator

The arithmetic mean is the sum of all values divided by the count of values. For {4, 8, 15, 16, 23, 42} the sum is 108 and the mean is 108 / 6 = 18. It is the most widely used measure of central tendency and is used in everyday contexts such as grade averages, average temperature, and average income.

The median is the middle value of a sorted data set. For an odd number of elements it is the single middle value; for an even number it is the average of the two middle values. The median is preferred over the mean when the data contains outliers. For example, if four people earn 3,000 and one earns 100,000, the mean is 22,800 but the median is 3,000 — which better represents the typical earner.

The mode is the value (or values) that appear most frequently in the data set. In {1, 2, 2, 3, 4} the mode is 2, because it appears twice. "None" means every value appears exactly once — the set has no mode. The mode is useful for categorical analysis, for example to find the most popular shoe size sold.

The range is the difference between the maximum and minimum values: R = max - min. For {4, 8, 15, 16, 23, 42} the range is 42 - 4 = 38. It is the simplest measure of dispersion — a large range means the values are widely spread. Its main weakness is sensitivity to outliers: a single extreme value can distort the picture.

When the data set has an even number of elements, the median is the average of the two middle values of the sorted set. For {1, 3, 5, 7} the median = (3 + 5) / 2 = 4. The mean is calculated as always: (1 + 3 + 5 + 7) / 4 = 4. In this case both measures are equal, which happens with symmetric distributions.

When two or more values share the highest frequency, the calculator lists all of them separated by a semicolon. For example {1, 1, 2, 2, 3} yields modes "1; 2". A bimodal data set can suggest two distinct groups in the data — often a signal for deeper analysis or segmentation.

The mean is very sensitive to outliers — one extreme value can shift the result significantly. The median is robust to outliers because it depends only on the position of the middle element. The mode is also unaffected by single extreme values. The range is the most sensitive measure, as it depends entirely on the minimum and maximum values.

For the mean and sum, the order makes no difference. For the median, the calculator sorts the set automatically before calculating, so you can enter numbers in any order. The mode is also independent of order. Numbers can be separated by commas or spaces — the calculator recognises both formats.

The sum is the total of all entered numbers, useful for checking total revenue or expenses. The count (n) shows how many numbers were recognised and included in the calculations — it helps catch data-entry errors. Both values are fundamental to descriptive statistics and are needed to calculate standard deviation and variance.

Mean, median and mode are the foundation of descriptive statistics. School grade averages, weekly average temperature, median salary in official reports, the most popular clothing size sold — these are just a few examples. In social sciences and medicine the median often replaces the mean for skewed distributions. The range gives a quick sense of data variability without complex calculations.