Statistics Interview Questions For Data Science and Analytics

Descriptive statistics summarize a dataset (mean, median, standard deviation, charts). Inferential statistics use a sample to draw conclusions about a larger population, using tools like confidence intervals and hypothesis tests.

The mean is the average, the median is the middle value when sorted, and the mode is the most frequent value. The median is more robust to outliers, so it's often preferred for skewed data like income.

Variance measures how far values spread from the mean (the average squared deviation). Standard deviation is its square root, in the same units as the data, making it easier to interpret as typical distance from the mean.

A normal (Gaussian) distribution is a symmetric, bell-shaped curve defined by its mean and standard deviation. About 68%, 95%, and 99.7% of values fall within one, two, and three standard deviations of the mean (the empirical rule).

A p-value is the probability of seeing a result at least as extreme as the observed one if the null hypothesis were true. A small p-value (commonly < 0.05) suggests the result is unlikely under the null, so you reject it. It is not the probability the null is true.

Hypothesis testing evaluates a claim about a population using sample data. You state a null and alternative hypothesis, pick a significance level, compute a test statistic and p-value, and either reject or fail to reject the null.

A Type I error is a false positive — rejecting a true null hypothesis. A Type II error is a false negative — failing to reject a false null. The significance level controls Type I risk; sample size and effect size affect Type II risk.

Correlation means two variables move together; causation means one actually drives the other. Correlation can arise from coincidence or a hidden confounding variable, so a correlation alone never proves cause — controlled experiments do.

The Central Limit Theorem states that the sampling distribution of the mean approaches a normal distribution as sample size grows, regardless of the population's shape. It's why we can use normal-based inference on means even for non-normal data.

A confidence interval is a range, computed from a sample, that is likely to contain the true population parameter. A 95% confidence interval means that if we repeated the sampling many times, about 95% of such intervals would contain the true value.

An A/B test randomly splits users into a control and a variant, exposes each to one version, and compares a metric with a hypothesis test. Randomization removes bias, and you need enough sample size and a fixed stopping rule to trust the result.

The population is every member of the group you care about; a sample is the subset you actually measure. Statistics infer population properties from a representative, randomly drawn sample to avoid bias.

Skewness measures the asymmetry of a distribution. Right (positive) skew has a long right tail and mean > median; left (negative) skew is the opposite. Skew signals when the median or a transformation may describe the data better than the mean.

First understand whether an outlier is an error or a real extreme value. Options include correcting or removing genuine errors, capping/winsorizing, transforming the data (e.g. log), or using robust methods like the median. Never drop points just because they're inconvenient.