Data Science interview questions and answers

The central limit theorem says that the sampling distribution of the mean becomes approximately normal as sample size grows, under mild conditions, even if the raw data are not normal.

A confidence interval is a range computed from sample data so that, in repeated sampling, a stated fraction of such intervals would cover the true parameter.

The IQR is the 75th percentile minus the 25th percentile, the spread of the middle half of the data.

Covariance measures joint variability in original units and can be any real number, so its size is hard to compare across metrics.

A z-score subtracts the mean and divides by the standard deviation so values are in standard-deviation units.

Bayes' theorem updates a prior probability of a hypothesis using the likelihood of new evidence, yielding a posterior.

Conditional probability P(A given B) is the chance of A restricted to the world where B occurred, equal to P(A and B) divided by P(B) when P(B) is positive.

Expected value is the probability-weighted average of a random payoff.

The law of large numbers says sample averages converge to the expected value as independent observations accumulate.

Mutually exclusive events cannot occur together, so their intersection probability is zero.

Use a t-test when the variance is estimated from the sample, especially with modest n, because the t distribution has heavier tails.

A two-tailed test flags large deviations in either direction

A chi-square test of independence checks whether two categorical variables are associated in a contingency table.

One-way ANOVA tests whether three or more group means differ, under normality and similar variance assumptions.

Power is the probability of rejecting the null when a specified alternative is true, equal to one minus the Type II error rate.

A tiny effect can be highly significant in a huge sample, and a large effect can miss significance in a small sample.

People treat p as the probability the null is true, or as the probability the result is a fluke in an informal sense.

For a symmetric null distribution, the two-sided p-value is typically twice the one-sided p-value from the observed direction, capped at 1.

P-hacking is trying many analyses, metrics, segments, or stopping times until a significant p-value appears, then reporting that path as if it were planned.

Sample size depends on baseline rate, minimum effect you care about, variance, alpha, and desired power.