Mean, Median, Mode Calculator
Calculate all measures of central tendency instantly. Get mean (average), median (middle value), mode (most frequent), and range with detailed explanations.
Central Tendency Calculator
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Enter data points to calculate mean, median, and mode
Understanding Central Tendency
Measures of central tendency are statistical values that describe the center or typical value of a dataset. The three main measures—mean, median, and mode—each provide different insights about your data's distribution and central point.
Mean (Average)
The mean is the arithmetic average of all values. It's calculated by adding all numbers and dividing by the count of numbers.
Example: For data [10, 20, 30, 40, 50]
Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30
✓ Best For:
- • Normally distributed data
- • Data without extreme outliers
- • When you need precise calculations
- • Most common scientific analyses
✗ Limitations:
- • Sensitive to extreme values
- • Can be misleading with skewed data
- • May not represent "typical" value
- • Affected by every data point
Median (Middle Value)
The median is the middle value when data is arranged in order. For even-sized datasets, it's the average of the two middle numbers.
Odd number of values:
[10, 20, 30, 40, 50] → Median = 30
Even number of values:
[10, 20, 30, 40, 50, 60] → Median = (30 + 40) / 2 = 35
✓ Best For:
- • Skewed distributions
- • Data with outliers
- • Income/salary data
- • Real estate prices
✗ Limitations:
- • Ignores actual values (only position)
- • Less useful for further calculations
- • Can't be used algebraically
- • Requires sorted data
Mode (Most Frequent)
The mode is the value that appears most frequently in the dataset. A dataset can have no mode, one mode (unimodal), or multiple modes (bimodal, multimodal).
Unimodal: [1, 2, 2, 2, 3, 4] → Mode = 2
Bimodal: [1, 1, 2, 3, 3] → Modes = 1 and 3
No mode: [1, 2, 3, 4, 5] → No repeating values
✓ Best For:
- • Categorical data
- • Finding most popular item
- • Discrete data
- • Quality control
✗ Limitations:
- • May not exist
- • Can have multiple values
- • Less useful for continuous data
- • Doesn't use all data points
Range (Spread)
The range is the difference between the maximum and minimum values, showing the spread of your data.
Example: For data [10, 20, 30, 40, 50]
Range = 50 - 10 = 40
When to Use Each Measure
Use Mean For:
- ✓ Evenly distributed data
- ✓ Scientific measurements
- ✓ Test scores (without curve breakers)
- ✓ Temperature readings
- ✓ Manufacturing tolerances
Use Median For:
- ✓ Income/salary data
- ✓ House prices
- ✓ Data with outliers
- ✓ Skewed distributions
- ✓ Ordinal data
Use Mode For:
- ✓ Favorite colors/products
- ✓ Shoe sizes
- ✓ Survey responses
- ✓ Most common defect type
- ✓ Categorical data
Real-World Examples
Example 1: Student Test Scores
Scores: [65, 72, 78, 85, 85, 88, 90, 92, 95, 100]
Average performance
Middle student's score
Most common score
All three measures are similar, indicating a balanced distribution with most students performing well.
Example 2: Employee Salaries
Salaries: [$35k, $40k, $42k, $45k, $48k, $50k, $55k, $250k (CEO)]
Skewed by CEO salary
Better representation ✓
All salaries unique
Median is most appropriate here as it's not affected by the CEO's outlier salary.
Frequently Asked Questions
What's the difference between mean and average?
Mean and average are the same thing - the arithmetic mean is calculated by adding all values and dividing by the count. However, "average" can technically refer to mean, median, or mode.
Which is better: mean or median?
Neither is universally "better." Use mean for normally distributed data without outliers. Use median for skewed data or when outliers are present (like income or house prices).
Can a dataset have more than one mode?
Yes! A dataset with two modes is called bimodal, and one with more than two is multimodal. If all values appear with equal frequency, there is no mode.
How do outliers affect these measures?
Mean is highly sensitive to outliers. Median is resistant to outliers. Mode is unaffected by outliers unless the outlier value is the most frequent. This is why median is preferred for data with extreme values.