How this tool fits your workflow
Mean vs median: which average to report
The arithmetic mean is sensitive to outliers. A salary dataset where most employees earn $50,000-$80,000 but the CEO earns $5,000,000 will have a mean far above the typical salary. The median is unaffected by that outlier and better represents the typical worker.
Use mean when the distribution is roughly symmetric with no extreme outliers. Use median when the distribution is skewed or contains outliers. Use mode when the most common value matters, such as product sizes or category choices.
Standard deviation in practice
Two datasets can have the same mean but very different standard deviations. Test scores: class A has mean 75 with SD 5 (most scores 70-80); class B has mean 75 with SD 20 (scores range 35-95). The means are identical but the distributions are completely different.
Population SD divides by N; sample SD divides by N-1 (Bessel's correction). The calculator uses sample SD for datasets smaller than the full population, which is appropriate for most real-world samples.
Frequently asked questions
- What is the difference between mean, median, and mode?
- Mean is the arithmetic average (sum divided by count). Median is the middle value when sorted — robust to outliers. Mode is the most frequently occurring value.
- What is standard deviation?
- Standard deviation measures how spread out values are around the mean. Small SD means values cluster close to the mean. Large SD means values are widely spread. About 68% of values fall within one SD of the mean in a normal distribution.
- What is the range?
- Range is the difference between the maximum and minimum values in a dataset. It is the simplest measure of spread but sensitive to outliers.
- How do I find the average of a list of numbers?
- Sum all numbers and divide by the count. For 4, 8, 15, 16, 23, 42: sum = 108, count = 6, mean = 18. Paste any list into the calculator for instant results.