Average Calculator
Types of Averages
Arithmetic Mean
Sum of values divided by count. Most common "average".
Median
Middle value when sorted. Less affected by outliers.
Mode
Most frequently occurring value(s).
Geometric Mean
Nth root of product. Used for growth rates.
Types of Averages
Related Calculators
Understanding Averages
What is an Average?
An average is a single value that represents or summarizes a set of data. There are several types of averages, each useful in different situations. The most common is the arithmetic mean, but median and mode are equally important in statistics.
Arithmetic Mean
Formula
Add all values and divide by the count. This is what most people mean by "average."
Example
Mean = (10 + 15 + 20 + 25 + 30) / 5 = 100 / 5 = 20
Median
The median is the middle value when data is sorted. If there's an even number of values, the median is the average of the two middle values.
When to Use Median
Median is often better than mean when data has outliers. For example, if 9 people earn $50,000 and 1 person earns $1,000,000, the mean is $145,000 but the median is $50,000 - which better represents the typical person.
Odd Count
Median = 9 (middle value)
Even Count
Median = (7 + 12) / 2 = 9.5
Mode
The mode is the value that appears most frequently. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal, multimodal).
Mode = 4 (appears 3 times)
Other Types of Averages
Weighted Mean
Each value is multiplied by its weight before summing. Used when some values are more important than others (e.g., course grades with credit hours).
Geometric Mean
The nth root of the product of n values. Best for averaging rates, ratios, and percentages (like investment returns).
Harmonic Mean
The reciprocal of the arithmetic mean of reciprocals. Best for averaging rates like speed (mph when traveling equal distances).
Trimmed Mean
Mean after removing a percentage of extreme values from both ends. Reduces influence of outliers while still using most data.
Choosing the Right Average
| Situation | Best Average | Why |
|---|---|---|
| Test scores | Mean | Balanced distribution, no extreme outliers |
| Home prices | Median | Outliers (mansions) skew the mean |
| Shoe sizes sold | Mode | Most popular size matters for inventory |
| Investment returns | Geometric | Accounts for compounding effect |
| Average speed | Harmonic | When rates apply to equal distances |
Key Insight
For any dataset: Geometric Mean ≤ Arithmetic Mean (always). The difference between them increases with data variability. For identical values, all three (arithmetic, geometric, harmonic) are equal.
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the sum of all values divided by the count (arithmetic average). Median is the middle value when data is sorted. Mode is the value that appears most frequently. Each measures central tendency differently and is useful in different situations.
When should I use median instead of mean?
Use median when your data has outliers or is skewed. For example, median income is more representative than mean income because a few billionaires can dramatically raise the average. Median is resistant to extreme values.
What is a weighted average and when do I use it?
A weighted average assigns different importance (weights) to each value. Use it when some values matter more than others, like calculating your GPA where a 4-credit course counts more than a 2-credit course.
Can a dataset have more than one mode?
Yes. A dataset with one mode is unimodal, two modes is bimodal, and multiple modes is multimodal. If all values appear with equal frequency, the dataset has no mode.