Statistics Basics

You do not need much statistics for a data interview. You need a small set of ideas stated precisely, because the questions are usually testing whether you can state them precisely.

Mean versus median. The mean is pulled by outliers; the median is not. Income, session duration, and revenue per user are all right-skewed, so the mean sits well above the typical experience. If someone quotes an average for skewed data, the median is the more honest number — and the distribution is more honest than either.

A p-value is the probability of observing a result at least this extreme *if the null hypothesis were true*. It is not the probability that the null hypothesis is true, and it is not the probability your result happened by chance. Getting this wrong is the single most common statistics error in interviews, and stating it correctly is a strong signal.

Type I error is a false positive: concluding there is an effect when there is not. Type II is a false negative: missing a real effect. Power is the probability of detecting an effect that genuinely exists, and it is what sample size buys you.

A 95% confidence interval means that if you repeated the procedure many times, about 95% of the intervals produced would contain the true value. It is a statement about the procedure, not a 95% probability that this particular interval contains it.

Correlation is not causation, and the specific reasons matter more than the slogan: there may be a confounder driving both, the direction may be reversed, or the sample may be selected in a way that manufactures the relationship.

Simpson's paradox is when a trend present in every subgroup reverses in the aggregate, usually because group sizes differ. It is the reason "always check the segments" is good advice rather than a platitude.

Survivorship bias is drawing conclusions from the things that made it through — studying successful startups tells you little without the failures that did the same things.