Every average, from one data set.
Paste your numbers and see the whole picture at once: the arithmetic mean everyone calls "the average", plus the median, the mode, and the geometric and harmonic means, with a dot plot that shows exactly where each one lands.
Your data set
One value per number. Decimals and negatives are fine, for example 85, 90, 78, 92, 88.
5 values entered.
Which average should you trust?
Where your numbers land
Dot plot of the sorted data
The full readout
Sorted data and frequency
Values sorted low to high. The frequency column counts how many times each value appears, which is how the mode is found.
| # | Value | Frequency | Running sum | Note |
|---|
Averages, explained
How to Calculate an Average
The arithmetic mean (average) is calculated by adding all numbers together and dividing by the count. For example, the average of 85, 90, 78, 92, and 88 is (85 + 90 + 78 + 92 + 88) / 5 = 86.6. This is the most commonly used measure of central tendency.
Types of Averages
Besides the arithmetic mean, there are other types of averages. The weighted average assigns different importance to values. The geometric mean multiplies values and takes the nth root, useful for growth rates. The harmonic mean is used for rates and ratios. Each serves different analytical purposes.
When the Average Can Be Misleading
The average is sensitive to outliers. If most employees earn $50,000 but the CEO earns $5,000,000, the average salary will be misleadingly high. In such cases, the median (middle value) often gives a better picture of typical values in the dataset.
Practical Uses of Averages
Averages are used everywhere, calculating grade point averages, batting averages in sports, average temperature over time, average cost of goods, and investment returns. Understanding when and how to use averages is a fundamental skill in data literacy.
Common questions
What is the difference between mean and average?
In common usage, "average" and "mean" are interchangeable and refer to the arithmetic mean. Technically, "average" is a broader term that can include median and mode as well.
Should I include zeros in my average?
It depends on whether zeros represent actual data points or missing values. This calculator treats 0 entries as "skip" to give you flexibility. If zero is a real data point, consider using a different value to mark empty fields.
How is a weighted average different?
A weighted average multiplies each value by a weight (importance factor) before summing, then divides by the total weight. For example, a final exam worth 40% of your grade carries more weight than homework worth 10%.
Can I calculate the average of negative numbers?
Yes. The average formula works with negative numbers. Simply add all values (including negatives) and divide by the count.
Results are computed from the exact numbers you enter. The geometric mean needs all positive values and the harmonic mean needs non-zero values, so those figures are shown only when your data allows them. Check your data set before relying on any single average.