Average Calculator (Mean, Median, Mode)
Average Calculator
The average calculator computes three measures of central tendency — mean, median, and mode — to summarize a dataset with a single representative value.
Conversion Formula
Mean = sum of all values ÷ count. Median = middle value after sorting (or average of two middle values). Mode = value(s) that appear most often.
Step-by-Step Examples
85, 90, 78, 92, 88 = Mean: 86.6, Median: 88, Mode: No mode
All values are unique, so there is no mode.
2, 4, 4, 6, 8 = Mean: 4.8, Median: 4, Mode: 4
4 appears twice, making it the mode.
10, 20, 30 = Mean: 20, Median: 20, Mode: No mode
When mean equals median, the data is symmetric.
History
The concept of the arithmetic mean dates back to the Pythagoreans in ancient Greece. The term "average" comes from Arabic "awar" (damage to goods), used in maritime insurance.
Common Use Cases
- Grade calculation
- Sports statistics
- Business performance metrics
- Scientific data analysis
- Survey result interpretation
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. Mode is the most frequently occurring value.
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 skew the mean.
Can there be more than one mode?
Yes. A dataset with two modes is bimodal, three modes is trimodal, and more than three is multimodal.
What if no number repeats?
If every value appears exactly once, there is no mode.
How do you find the median of an even number of values?
Sort the values and average the two middle numbers. For example, in {2, 4, 6, 8}, the median is (4 + 6) / 2 = 5.
What is a weighted average?
A weighted average multiplies each value by a weight before summing, then divides by the total weight. It is useful when some values matter more than others.
Can the mean be a decimal even if all inputs are integers?
Yes. For example, the mean of 1, 2, 4 is 2.333, which is not an integer.
What is the difference between population mean and sample mean?
Population mean uses all data points; sample mean uses a subset. The formulas are the same, but the distinction matters for statistical inference.