What are mean, median, and mode?
Mean, median, and mode are three fundamental measures of central tendency in statistics. The mean (arithmetic average) is calculated by adding all numbers and dividing by the count. The median is the middle value when numbers are sorted in ascending order. The mode is the most frequently occurring value in a data set.
How to calculate the mean?
The mean formula: Mean = (x₁ + x₂ + ... + xₙ) / n. For example, the mean of 4, 8, and 12 is (4 + 8 + 12) ÷ 3 = 8. The mean is sensitive to outliers — a single very large or small value can significantly affect the result.
How to find the median?
To find the median, sort the numbers in ascending order and select the middle value. If there is an even number of values, the median is the average of the two middle values. For example, the median of 3, 7, 9 is 7, while the median of 2, 4, 6, 8 is (4 + 6) ÷ 2 = 5.
How to determine the mode?
The mode is the value that appears most frequently in a data set. A data set can have one mode, multiple modes, or no mode at all (when all values are unique). For example, in the set 2, 3, 3, 5, 7, the mode is 3 because it appears twice.
Mean, median, and mode calculation example
Data set: 10, 15, 15, 20, 25, 30, 100. Mean: (10+15+15+20+25+30+100) / 7 = 30.7. Median: 20 (middle value). Mode: 15 (appears 2 times). This example shows how extreme values (100) affect the mean but not the median.
When to use mean, median, or mode?
The mean works best when data is evenly distributed without extreme outliers. The median better represents the typical value when data contains significant outliers — for example, when analyzing salaries or real estate prices. The mode is useful for categorical data and identifying the most popular value.