Mean, Median, Mode, Range Calculator
Calculate descriptive statistics including mean (average), median (middle value), mode (most frequent), and range (spread) for any dataset.
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Quick Examples
Data Summary
Statistical Results
Additional Statistics
How to Use This Calculator
This calculator computes the four main measures of central tendency and spread for your dataset:
- Choose your preferred input method (manual entry, comma-separated list, or frequency table)
- Enter your numerical data using the selected method
- View the calculated mean, median, mode, and range instantly
- Explore additional statistics and frequency distribution
- Use the sort function to organize your data or clear to start over
Understanding Descriptive Statistics
Mean (Average)
The mean is the sum of all values divided by the number of values. It represents the typical value in your dataset and is sensitive to extreme values (outliers).
Formula: Mean = (Sum of all values) ÷ (Number of values)
Median (Middle Value)
The median is the middle value when data is arranged in order. If there's an even number of values, it's the average of the two middle values. The median is less affected by outliers than the mean.
Mode (Most Frequent)
The mode is the value that appears most frequently in the dataset. A dataset can have:
- No mode: All values appear with the same frequency
- One mode (unimodal): One value appears most frequently
- Multiple modes (multimodal): Two or more values tie for highest frequency
Range (Spread)
The range is the difference between the maximum and minimum values in the dataset. It gives you an idea of how spread out your data is.
Formula: Range = Maximum value - Minimum value
When to Use Each Measure
- Mean: Best for normally distributed data without extreme outliers
- Median: Better for skewed data or when outliers are present
- Mode: Useful for categorical data or finding the most common value
- Range: Quick measure of variability, but sensitive to outliers
Example Calculations
Example 1: Test Scores
Dataset: 85, 92, 78, 96, 88, 91, 85
- Mean: (85+92+78+96+88+91+85) ÷ 7 = 87.86
- Median: Sorted: 78, 85, 85, 88, 91, 92, 96 → Middle value = 88
- Mode: 85 (appears twice)
- Range: 96 - 78 = 18
Example 2: Ages
Dataset: 25, 30, 35, 25, 40, 30, 25, 45
- Mean: (25+30+35+25+40+30+25+45) ÷ 8 = 31.875
- Median: Sorted: 25, 25, 25, 30, 30, 35, 40, 45 → (30+30) ÷ 2 = 30
- Mode: 25 (appears three times)
- Range: 45 - 25 = 20
Example 3: No Mode
Dataset: 10, 20, 30, 40, 50
- Mean: (10+20+30+40+50) ÷ 5 = 30
- Median: 30 (middle value)
- Mode: No mode (all values appear once)
- Range: 50 - 10 = 40
Frequently Asked Questions
What's the difference between mean and median?
The mean is the arithmetic average of all values, while the median is the middle value when data is sorted. The median is less affected by extreme values (outliers) and is often a better measure of central tendency for skewed data.
Can a dataset have multiple modes?
Yes! A dataset can be unimodal (one mode), bimodal (two modes), multimodal (more than two modes), or have no mode if all values appear with the same frequency.
How do outliers affect these statistics?
Outliers significantly affect the mean and range but have little impact on the median and mode. This is why the median is often preferred when dealing with skewed data or datasets with extreme values.
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