Calculate Average, Median, Mode with Step-by-Step Derivation
Enter numbers separated by commas
Results
Mean
Median
Mode
Range
Step-by-Step Derivation
Formulas
Mean = (Sum of all values) / (Number of values)
Median = Middle value when sorted (average of two middle values if even count)
Mode = Most frequently occurring value(s)
Range = Max value - Min value
Mean, median, and mode are measures of central tendency. Range measures data spread.
⚠Enter numbers separated by commas. Supports integers and decimals. Maximum 50 values.
What are Mean, Median & Mode?
These are measures of central tendency that describe the center of a dataset. Mean is the average, median is the middle value, and mode is the most frequent value.
Mean (Average)
Sum of all values divided by count. Sensitive to outliers. Example: 1,2,3 → Mean = 2.
Median
Middle value when sorted. Robust to outliers. Example: 1,2,3,4 → Median = 2.5.
Mode
Most frequent value. Can be multiple. Example: 1,2,2,3 → Mode = 2.
Range
Difference between max and min. Measures spread. Example: 1,2,3,4,5 → Range = 4.
💡 Example: Data: 1, 2, 3, 4, 5, 5, 6. Mean = 26/7 ≈ 3.71, Median = 4, Mode = 5, Range = 5.
Applications
Data AnalysisStatisticsFinanceEducationResearch
Frequently Asked Questions
What is the difference between mean, median, and mode?▼
Mean is the average value, median is the middle value when sorted, and mode is the most frequently occurring value. Mean is affected by outliers, median is robust to outliers, mode works for categorical data.
When should I use median instead of mean?▼
Use median when your data has outliers or is skewed. For example, income data is often skewed, so median income is a better representation than mean income.
Can there be more than one mode?▼
Yes, a dataset can have multiple modes. If two values occur with the same highest frequency, it is bimodal. If more than two values have the same highest frequency, it is multimodal.
What is range in statistics?▼
Range is the difference between the maximum and minimum values in a dataset. It measures the spread of the data: Range = Max - Min.
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