How to describe a data set before analysing it
Always start with centre and spread. The Mean, Median, Mode Calculator gives all three measures of centre at once, which is the fastest way to spot skew — when the mean sits well above the median, a few large values are pulling it.
Then look at dispersion. The Standard Deviation Calculator quantifies spread around the mean, while the Five Number Summary Calculator and Interquartile Range Calculator describe it in a way outliers cannot distort. If you suspect extreme values, the Outlier Calculator applies the standard 1.5×IQR rule and flags the specific values falling outside it.
When to use sample versus population formulas
This choice changes your answer, and it trips up almost everyone at least once. If your numbers are the entire group you care about, use the population formula. If they are a sample drawn from a larger group and you want to estimate that group's spread, use the sample formula, which divides by n−1 rather than n.
That correction, Bessel's correction, exists because a sample tends to understate true variability. Both the Standard Deviation Calculator and Variance Calculator let you pick. The Standard Error Calculator then tells you how precisely your sample mean estimates the population mean.
How to size a survey and read the result
Decide precision first, then work back to numbers. The Sample Size Calculator tells you how many responses a chosen margin of error and confidence level require — and the answer depends far less on population size than people assume, which is why national polls work with about 1,000 people.
Once data is in, the Margin of Error Calculator and Confidence Interval Calculator express the uncertainty honestly. For relationships between two variables, the Correlation Coefficient Calculator gives r, and the Coefficient of Determination Calculator gives R², the share of variance explained.
Frequently asked questions
- When should I use the median instead of the mean?
- Use the median when the data is skewed or contains extreme values, since it is not dragged by outliers. Income is the classic example — a handful of very high earners pull the mean well above what a typical person earns.
- What is the difference between sample and population standard deviation?
- The population version divides by n; the sample version divides by n−1 to correct for the fact that samples underestimate true spread. Use the sample formula whenever your data is a subset you are generalising from.
- What does a p-value actually mean?
- It is the probability of seeing a result at least as extreme as yours if the null hypothesis were true. It is not the probability that your hypothesis is correct, and a p-value below 0.05 is a convention, not proof.
- How many people do I need for a survey?
- Around 385 responses give a ±5% margin of error at 95% confidence for any large population, and about 1,067 give ±3%. Population size barely matters once it is above roughly 20,000.
- Does correlation mean causation?
- No — a correlation coefficient only measures how closely two variables move together, not why. A third variable can drive both, or the relationship can be coincidence, especially in small samples.