Average Calculator
Calculate mean, median, mode, range, and standard deviation for any set of numbers — with a complete statistical summary.
Example Output
Input: 85, 92, 78, 96, 88, 74, 91
- Mean: 86.29
- Median: 88
- Mode: No Mode
- Range: 22
- Min: 74
- Max: 96
- Std Dev: 7.30
- Sum: 604
Frequently Asked Questions
What is the difference between mean median and mode?
The mean is the arithmetic average found by adding all values and dividing by the count. The median is the middle value when numbers are sorted — less affected by outliers. The mode is the most frequently occurring value. For example in a class of test scores the mean gives the overall average but the median better represents typical performance if a few very high or low scores skew the mean.
When should I use median instead of mean?
Use median when data has extreme outliers that would distort the average. Home prices and income statistics use median rather than mean because a few very wealthy individuals or expensive properties would make the mean much higher than what a typical person earns or pays. Median splits the data in half with equal numbers above and below.
What is standard deviation?
Standard deviation measures how spread out numbers are from the mean. A low standard deviation means values cluster close to the mean. A high standard deviation means values are spread widely. For example two classes could have the same mean test score of 80 but one class has scores ranging from 75 to 85 (low std dev) while another ranges from 50 to 100 (high std dev).
What is the difference between population and sample standard deviation?
Population standard deviation divides by n (the total count) and is used when you have data for the entire group. Sample standard deviation divides by n-1 and is used when your data is a sample from a larger population. The n-1 correction (Bessel's correction) gives a better estimate of the true population variance. Most calculators and statistics courses use sample standard deviation.
What are geometric and harmonic means used for?
Geometric mean is used for growth rates investment returns and ratios — multiplying values then taking the nth root. For example average investment return over multiple years uses geometric mean to account for compounding. Harmonic mean is used for rates and ratios like average speed — if you drive 60 mph there and 40 mph back the harmonic mean gives the true average speed not the arithmetic mean.