Mean, Median, Mode Calculator
Calculate measures of central tendency for your dataset
Mean = Σx / n
Average
Median = Middle
Central value
Mode = Most Frequent
Common value
Minimum 1 number required
Quick Examples
Mean (Average)
Median (Middle)
Mode (Most Frequent)
None
Count (n)
Sum (Σx)
Min
Max
Range
Step-by-Step Breakdown
Step 1: Your Data
Step 2: Calculate Mean
Mean = () / =
Step 3: Calculate Median
Sorted:
Middle value = Average of middle values =
Step 4: Find Mode
All values appear only once → No mode
Most frequent value(s) →
Note: Step-by-step breakdown is hidden for datasets larger than 10 values for readability.
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About Mean, Median, Mode Calculator
What are Mean, Median, and Mode?
Mean, median, and mode are the three most common measures of central tendency in statistics. Each provides a different way to describe the "center" or typical value of a dataset.
Understanding Each Measure
Mean (Average)
The mean is calculated by summing all values and dividing by the count. It's sensitive to outliers and best for normally distributed data.
Formula: Mean = Σx / n
Median (Middle Value)
The median is the middle value when data is sorted. For even-count datasets, it's the average of the two middle values. It's resistant to outliers.
Formula:
- Odd n: Middle value at position (n+1)/2
- Even n: Average of values at positions n/2 and (n/2)+1
Mode (Most Frequent)
The mode is the value that appears most frequently. A dataset can have:
- No mode - all values appear equally often
- Unimodal - one mode
- Bimodal - two modes
- Multimodal - three or more modes
When to Use Each Measure
| Measure | Best For | Avoid When |
|---|---|---|
| Mean | Normally distributed data | Outliers present |
| Median | Skewed data, ordinal data | Categorical data |
| Mode | Categorical data, finding typical values | All values unique |
Example Calculation
Dataset: 2, 3, 3, 5, 7, 9, 10
- Mean: (2+3+3+5+7+9+10) / 7 = 39 / 7 ≈ 5.57
- Median: Middle value (4th value) = 5
- Mode: 3 (appears twice)
Practical Applications
- Education - Average test scores, grade distributions
- Business - Average sales, typical customer spending
- Research - Data analysis, survey results
- Finance - Average returns, typical transaction amounts
- Quality Control - Process measurements, defect rates
Tip: Use all three measures together for a complete picture of your data's central tendency. If they differ significantly, your data may be skewed.