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Average Calculator (Mean, Median, Mode & Range)
In statistics and mathematics, the central tendency of a dataset describes the typical or central value around which data points cluster. This statistical calculator computes the arithmetic mean, finds the median middle value, identifies the mode frequency, and determines the range dispersion for any sequence of numbers.
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How to Use This Tool Step-by-Step
- Enter your numbers separated by commas or spaces (e.g. 14, 28, 35, 42, 50).
- Click Calculate to evaluate statistical measures.
- Review the Mean, Median, Mode, Range, Sum, and Count with full working steps.
📐 Statistical Definitions & Formulas
• Arithmetic Mean: Sum of all values divided by total count: μ = (Σx) ÷ n • Median: Middle number when dataset is sorted in numerical order (average of two middle numbers if n is even). • Mode: The value that appears most frequently in the dataset. • Range: The difference between the highest and lowest value: Maximum - Minimum.
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Worked Statistical Example
Given data: 12, 15, 15, 20, 28
1. Count n = 5
2. Sum = 12 + 15 + 15 + 20 + 28 = 90
3. Mean = 90 ÷ 5 = 18.0
4. Median = 15 (third number in ordered sequence)
5. Mode = 15 (appears twice)
6. Range = 28 – 12 = 16.
📊 Reference Benchmarks & Classification Data
| Measure | Formula / Rule | Best Used When | Outlier Sensitivity |
|---|---|---|---|
| Mean | Sum ÷ Count | Data is symmetrically distributed | Highly sensitive to outliers |
| Median | Middle sorted value | Data contains extreme high/low values | Resistant to outliers |
| Mode | Most frequent value | Categorical or nominal data | Unaffected by extreme values |
| Range | Max – Min | Measuring total spread/dispersion | Extremely sensitive to extremes |
❓ Frequently Asked Questions (FAQ)
Why is the median often preferred over the mean for income statistics?
Average income can be skewed upward by a few multi-millionaires, giving a misleading impression of normal earnings. The median represents the exact middle person, providing a more realistic picture of typical household earnings.
Can a dataset have more than one mode?
Yes. A dataset with two values tied for the highest frequency is bimodal. If three or more values tie, it is multimodal. If all numbers occur with equal frequency, there is no mode.