How to Calculate Average (Mean)
Add all values together and divide by the count: Mean = Sum ÷ Count. Enter numbers separated by commas, spaces, or new lines for complete statistical analysis.
Example
Dataset: 4, 7, 2, 9, 3
- Mean: (4 + 7 + 2 + 9 + 3) ÷ 5 = 5.0
- Median: Sorted: 2, 3, 4, 7, 9 → middle value = 4
- Mode: No repeated values → no mode
- Range: 9 − 2 = 7
Statistics Measures Reference
Every measure this calculator reports, what it tells you, and how it is found. The first three are measures of center; the rest describe spread or serve specialized cases.
| Measure | What It Tells You | How It Is Found |
|---|---|---|
| Mean | Typical value; the balance point | Sum ÷ count |
| Median | Middle value; resists outliers | Middle of the sorted list |
| Mode | Most common value | Value with highest frequency |
| Range | Total spread | Maximum − minimum |
| Midrange | Rough center of the extremes | (Maximum + minimum) ÷ 2 |
| Variance | Average squared distance from the mean | Mean of squared deviations |
| Standard deviation | Typical distance from the mean | Square root of the variance |
| Sum | Combined total of all values | Add every value |
| Count | How many values are in the set | Tally of the entries |
| Weighted mean | Average when values carry different importance | Sum of value × weight ÷ total weight |
| Geometric mean | Average growth rate or ratio | nth root of the product of values |
| Harmonic mean | Average of rates and speeds | Count ÷ sum of reciprocals |
| Quartiles (Q1, Q3) | Values at the 25% and 75% marks | Medians of the lower and upper halves |
| Interquartile range | Spread of the middle 50% | Q3 − Q1 |
Understanding the Terms
Central Tendency
The single value that best represents a whole dataset. Mean, median, and mode are the three common measures — which one is "the average" depends on the shape of your data.
Dispersion
How spread out the values are. Range, variance, and standard deviation all describe dispersion; two datasets can share a mean yet differ wildly in spread.
Outlier
A value far from the rest of the set. Outliers drag the mean toward themselves but barely move the median, which is why median is preferred for skewed data like income.
Distribution
The pattern of how values are arranged. In a symmetric distribution the mean and median nearly match; in a skewed one they separate, with the mean pulled toward the long tail.
Population vs Sample
A population is every member of the group; a sample is a subset. Sample standard deviation divides by count minus one to correct for the smaller information in a subset.
Mean vs Median vs Mode
- Mean (arithmetic average): Sum ÷ count. Sensitive to outliers — one extreme value shifts it significantly
- Median (middle value): The value that splits the dataset in half when sorted. Resistant to outliers. For even-sized datasets, average the two middle values
- Mode (most frequent): The value that appears most often. A dataset can have multiple modes (bimodal, multimodal) or no mode at all
When to Use Each
- Mean: Symmetric data without outliers — test scores, heights, daily temperatures
- Median: Skewed data with outliers — household income, home prices, response times. Median US household income (~$80,000) is far more representative than the mean (~$115,000) because extreme earners skew the average
- Mode: Categorical or discrete data — most popular shoe size, most common survey response, most frequent error code
Standard Deviation
Measures how spread out values are from the mean. A low standard deviation means data is tightly clustered; a high one means data is spread wide.
- 68% of data falls within 1 SD of the mean
- 95% of data falls within 2 SDs of the mean
- 99.7% of data falls within 3 SDs of the mean
This "68-95-99.7 rule" applies to normally distributed data and is used in quality control, grading curves, and scientific research.
Other Types of Averages
- Weighted average: Values are multiplied by weights before summing. Used in GPA calculation (credits × grade points), portfolio returns, and overall course grades
- Geometric mean: The nth root of the product of n values. Used for average growth rates, investment returns, and ratios
- Harmonic mean: Reciprocal of the mean of reciprocals. Used for average speeds and rates
Related Math Calculators
- Mean, Median, Mode, Range Calculator — the core four measures with step-by-step work
- Percentage Calculator — percent of a total, percent change, and reverse percent
- GPA Calculator — a weighted average of course grades by credit hours
- Test Grade Calculator — score percentage and letter grade from correct answers
- Ratio Calculator — simplify, scale, and compare ratios and proportions