Calculate mean, median, mode, standard deviation, variance, and range instantly. Enter your data set and get complete statistical analysis. Free online statistics calculator with formula explanations.
So you've got a bunch of numbers and you need to make sense of them. Maybe it's your test scores, maybe it's sales data, or maybe it's just a homework problem. That's exactly what our Statistics Calculator is here for.
This tool does all the heavy lifting for you. You just type in your numbers, and it spits out the mean, median, mode, standard deviation, variance, range, and more. Plus, we explain what each one actually means.
Add up all numbers, divide by count. The most common way to find the "center." But watch out ā outliers can pull the mean misleadingly. Bill Gates in a room skews the average wealth.
Put numbers in order, pick the middle. Better than mean when data has outliers. For house prices, median is usually more meaningful than average.
The number that appears most often. Great for categorical data like "favorite color." Sometimes there's no mode or multiple modes.
How spread out numbers are from the mean. Small = tightly clustered. Large = all over the place. About 68% of data falls within 1 SD of the mean.
Standard deviation squared. Less intuitive but important for advanced statistics. SD is easier to understand because it's in the same units as your data.
Data for every single member of a group. Like measuring all 30 students in one class. Divide by n.
Data for only a subset. Like measuring 50 people to estimate all adults. Divide by n-1 for more accuracy.
Mean = 74, SD = 15. Scores are all over. Some got it, some didn't. Teacher reviews material before moving on.
Mean daily sales = $450, Median = $420. Difference shows weekends are much higher. Owner adjusts staffing.
High mean + low SD = consistently good player. High mean + high SD = streaky ā amazing some days, terrible others.
#1: Using mean when median is better. Outliers skew the mean. Use median for income, house prices, or any data with extremes.
#2: Confusing population and sample. Changes your SD and variance. Always double-check which one you need.
#3: Thinking high SD is bad. Variety isn't always bad. Sometimes spread is exactly what you want to see.
Variance is standard deviation squared. SD is easier to understand because it's in the same units as your data. Height in inches ā SD in inches. Variance would be inches squared.
Population = you have data for everyone. Sample = you have a subset. When in doubt, use sample ā it's more conservative.
Mean is the average. Median is the middle number. Mean gets pulled by outliers; median resists them. For incomes, median is usually better.
Every number appears exactly once. The mode only exists when some values repeat. This is normal for small or varied data sets.
Largest number minus smallest number. Simple but only uses two extremes and ignores everything in between.