Calculate mean, median, mode, and range for any set of numbers. Essential tool for statistics, data analysis, and understanding data distributions.
Mean
30.0000
Median
30.0000
Mode
None
Range
40.0000
Statistical averages are measures of central tendency that summarize a dataset with a single representative value. They help us understand the typical value in a set of data and are fundamental concepts in statistics and data analysis.
Different types of averages serve different purposes. The mean is best for numerical data without outliers, the median works better with skewed data or outliers, and the mode helps identify the most common value. The range shows how spread out the data is.
These statistics are used extensively in science, economics, engineering, healthcare, and business to make informed decisions based on data patterns and trends.
The arithmetic average. Calculated by adding all numbers and dividing by how many numbers there are. Best for data without extreme outliers.
The middle value when data is arranged in order. If even count, average the two middle values. Useful for skewed data with outliers.
The value that appears most often in the dataset. Can be "None" if all values appear equally, or multiple modes if tied.
The difference between the largest and smallest values. Shows how spread out or dispersed the data is.
Calculate all measures for: 2, 4, 4, 6, 9
Step 1: Mean
(2 + 4 + 4 + 6 + 9) ÷ 5 = 25 ÷ 5 = 5
Step 2: Median
Sorted: [2, 4, 4, 6, 9] → Middle value = 4
Step 3: Mode
Frequency: 2(×1), 4(×2), 6(×1), 9(×1) → Most frequent = 4
Step 4: Range
Max - Min = 9 - 2 = 7
Use the median when your data has 'outliers' (extremely high or low values) that would skew the mean unfairly. For example, average house prices in a neighborhood with one mansion.
Yes! If two values appear with the same highest frequency, the set is 'bimodal'. If more than two, it's 'multimodal'. If all unique, there's 'no mode'.
Take the average of the two middle values. For {3, 5, 7, 9}, the median is (5 + 7) ÷ 2 = 6.
For mean and mode, no. For median, the calculator automatically sorts the data. Range also works regardless of input order.
Mean is most affected by outliers (pulled toward extreme values). Median is resistant to outliers. Mode and range are unaffected unless the outlier is the most frequent or extreme value.
Yes! This calculator accepts any real numbers including negative values, decimals, and fractions. Scientific notation also works.
Range measures data spread. A small range means data is clustered close together. A large range means data is dispersed. It's useful for understanding variability.
Together they provide a complete picture: mean shows the center, median shows the middle for skewed data, mode shows frequency patterns, and range shows spread. Use all to fully understand data.