Mean, Median & Mode Calculator
Calculate mean, median, mode, range, and other statistics for any data set.
Mean, Median, and Mode Explained
These three measures of central tendency each tell a different story about your data:
- Mean (average): Sum of all values divided by count. Sensitive to outliers.
- Median: The middle value when sorted. Robust against outliers.
- Mode: The most frequently occurring value. Can have multiple modes or none.
Example: Data set 100. Mean = 22.6 (skewed by 100). Median = 3 (unaffected). Mode = 3. Here, median best represents the typical value.
When to Use Each Measure
Mean: Best for symmetric data without extreme outliers — test scores, heights, temperatures. Median: Best for skewed data — incomes (a few billionaires skew the mean), home prices, response times. Mode: Best for categorical data — most popular color, most common shoe size, most frequent defect type.
The relationship between them reveals distribution shape: if mean > median, data is right-skewed (positively skewed); if mean < median, left-skewed.
Standard Deviation and Spread
Central tendency alone is incomplete — you also need to know how spread out the data is. Standard deviation measures average distance from the mean. A small SD means data clusters tightly around the mean; a large SD means wide spread.
In a normal distribution: 68% of data falls within 1 SD of the mean, 95% within 2 SD, 99.7% within 3 SD (the 68-95-99.7 rule).
Frequently Asked Questions
Which is better: mean or median?
Neither is universally better. Median is more robust (not affected by extreme values). Mean uses all data points and is better for symmetric distributions. For income and housing data, median is preferred. For test scores and scientific measurements, mean is standard.
Can a data set have no mode?
Yes. If all values occur equally often, there is no mode. A data set can also be multimodal — having two modes (bimodal) or more. Example: 3 is bimodal with modes 1 and 3.
How do I find the median of an even number of values?
Sort the values, then average the two middle numbers. For 8: middle values are 4 and 6, so median = (4+6)/2 = 5.