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Understanding Mean, Median, Mode, and Range
These four measures describe a dataset. The mean is the arithmetic average. The median is the middle value when sorted. The mode is the most frequently occurring value. The range is the difference between the highest and lowest values. Together, they give a comprehensive summary of your data.
When to Use Each Measure
Use the mean for symmetrical data without outliers. Use the median when data is skewed or has outliers (like income data). The mode is useful for categorical data or finding the most common value. The range provides a quick sense of data spread but is sensitive to extreme values.
How to Find the Median
Sort all values from smallest to largest. If the count is odd, the median is the middle number. If even, the median is the average of the two middle numbers. For example, in {3, 5, 7, 9, 11}, the median is 7. In {3, 5, 7, 9}, the median is (5 + 7) / 2 = 6.
Multimodal Datasets
A dataset can have one mode (unimodal), two modes (bimodal), or more (multimodal). If no value repeats, there is no mode. Bimodal distributions often suggest two distinct groups in the data, which may warrant further investigation.
Frequently Asked Questions
If every value in the dataset appears exactly once, there is no mode. This calculator will report "No mode" in that case.
Yes. If two values tie for highest frequency, the dataset is bimodal. If three or more tie, it is multimodal. All modes will be reported.
Neither is universally better. The mean uses all values and works well for symmetric data. The median is more robust against outliers. For income data, housing prices, and skewed distributions, the median is generally more informative.
Range only considers the two extreme values and ignores everything in between. A single outlier can dramatically increase the range. Interquartile range (IQR) is a more robust measure of spread.