Data Scientist interview questions

Mean, median, and mode describe a dataset's center in different ways.

• Mean is the arithmetic average and works best for roughly symmetric data.
• Median is the middle sorted value and is robust to outliers and skew in data such as incomes or session durations.
• Mode is the most frequent value and suits categorical data such as device type.
• Reporting mean and median together helps reveal skew because a large gap warns that either number alone may mislead.

Variance and standard deviation both measure how widely values spread around the mean.

• Variance is the average squared deviation from the mean.
• Standard deviation is the square root of variance and uses the original units, such as dollars rather than squared dollars.
• Products with equal average sales but different standard deviations require different planning because the more volatile one needs more safety stock and careful forecasting.

Percentiles and the interquartile range describe position and spread without relying on a single average.

• The p-th percentile is the value below which p percent of observations fall, so a two-second 95th percentile latency means 95 percent of requests are faster.
• Quartiles are the 25th, 50th, and 75th percentiles.
• The interquartile range is the distance from the 25th to the 75th percentile and measures spread while ignoring extreme tails.
• Percentiles show what specific groups of users experience more clearly than an overall average.

A distribution is skewed when one tail is much longer than the other.

• Right skew is common in money and duration data.
• The long tail pulls the mean toward itself while the median remains more stable, so the mean may sit far above a typical observation under heavy right skew.
• Check the shape with a histogram before choosing a summary statistic or using the raw variable in a model that assumes symmetry.

The normal distribution is a symmetric bell-shaped distribution centered on its mean.

• About 68 percent of values lie within one standard deviation of the mean and about 95 percent lie within two.
• It appears often because sums and averages of many small independent effects tend toward normality under the central limit theorem.
• Measurement errors are a standard example of this pattern.
• Business metrics such as revenue and delays are often heavily skewed, so normality must be checked rather than assumed.

The central limit theorem says that sample means tend toward a normal distribution as the sample grows, regardless of the source distribution's shape.

• This behavior lets us build confidence intervals and tests for averages even when the original data is skewed.
• The approximation becomes useful only with enough observations.
• Small samples and heavy-tailed data can make it unreliable, so the theorem has conditions rather than being automatic.

A population is the full group of interest, while a sample is the subset actually observed.

• A good sample is representative, meaning every relevant part of the population has a fair chance of inclusion.
• Randomization helps provide that fair chance.
• Larger samples improve precision, but representativeness matters more because a biased sample of a million can answer the wrong question very precisely.

Sampling bias appears when observed data systematically excludes relevant parts of the population.

• Opt-in bias occurs when survey data includes only users who chose to respond.
• Survivorship bias occurs when a churn model sees only customers who stayed long enough to build a history and misses fast leavers.
• Generalizing weekday observations to weekends mixes different populations.
• Biased data can look perfectly clean, so ask how the data came to exist and who is missing before analyzing it.

Correlation shows that two variables move together, while causation means changing one actually changes the other.

• Ice cream sales correlate with drownings because summer affects both.
• Feature users may retain better because engaged users both use more features and stay longer, not because the feature causes retention.
• Observational data supports correlational claims, while causal claims need experiments such as A/B tests or careful causal methods.
• Confusing correlation with causation can lead to expensive wrong decisions.

Pearson's correlation coefficient measures the direction and strength of a linear relationship from minus one to one.

• The sign gives the direction, the magnitude gives the strength, and zero means no linear relationship.
• It misses nonlinear patterns, so even a perfect U-shaped relationship can have a value near zero.
• It is sensitive to outliers because one extreme point can create or destroy an apparent correlation.
• Always inspect a scatter plot because identical coefficients can hide very different relationships.

Simpson's paradox occurs when a trend seen in every subgroup reverses after the groups are combined.

• Different group sizes act as hidden weights in the aggregate result.
• For example, every department may admit women at a higher rate while the overall rate appears lower because women applied more often to competitive departments.
• Check important conclusions across meaningful segments before trusting an aggregate because changes in group composition can mislead dashboards.

Independent events do not change each other's probabilities, while conditional probability accounts for known information.

• For independent events, the joint probability equals the product of their individual probabilities.
• Conditional probability P(A given B) is the probability of A once B is known to have happened.
• Dependence means P(A given B) differs from P(A).
• Data science often asks conditional questions, such as churn probability given that a user stopped opening the app.

Bayes' theorem updates a prior belief with new evidence while accounting for how common the target condition is.

• The probability of a disease after a positive test depends on both test accuracy and disease prevalence.
• A 99 percent accurate test for a disease affecting one person in a thousand produces roughly ten false alarms for each true case because the healthy group is so large.
• Fraud detection and spam filtering follow the same logic, so rare targets can make even good classifiers generate many false positives.

A p-value measures how surprising the observed result would be if the null hypothesis were true.

• Formally, it is the probability of data at least as extreme as observed under the null hypothesis.
• It is neither the probability that the null hypothesis is true nor the probability that the finding matters.
• A tiny p-value can accompany a microscopic effect that is statistically significant but practically useless.
• Report effect size alongside the p-value to show practical importance.

A hypothesis test compares observed data with what the null hypothesis predicts under a threshold chosen in advance.

• Define a null hypothesis, usually no effect or difference, an alternative hypothesis, and a significance level such as 0.05 before viewing results.
• Calculate the p-value and reject the null in favor of the alternative when it falls below the threshold.
• A 0.05 threshold permits about one false alarm in twenty tests on pure noise.
• Running many tests without correction therefore creates false discoveries.

A 95 percent confidence interval expresses the precision of an estimate through a repeated-sampling procedure.

• Across repeated samples, intervals built this way would contain the true population value 95 percent of the time.
• A conversion estimate of 5.2 percent plus or minus 0.3 is much more precise than the same estimate plus or minus 3.
• Larger samples and lower variance produce narrower intervals.
• If a decision changes within the interval's range, the data does not yet support that decision firmly.

A trustworthy A/B test follows a plan set before launch and preserves random assignment.

• Random assignment should make the groups differ only by the treatment.
• Fix sample size and duration in advance with a power calculation instead of stopping when results look favorable.
• Declare one primary metric before launch rather than searching across many outcomes.
• Peeking, stopping early, nonrandom splits, and fishing across twenty metrics inflate false positives or break the comparison.

Outliers should be detected systematically and handled according to their cause.

• Use box plots, histograms, the 1.5 IQR rule, or extreme z-scores to find unusual observations.
• Fix or remove data errors, but keep genuine extremes such as a very large customer.
• Handle valid extremes with robust statistics, winsorization, or separate reporting when appropriate.
• Never silently delete points that spoil a preferred story because outliers may be the main finding.

A probability distribution describes the possible values of a random quantity and how likely they are.

• Discrete distributions cover countable outcomes such as purchases, clicks, or defects and assign probability to exact values.
• Continuous distributions cover measurements such as time or weight, where probability applies to intervals and is represented by a density.
• The distinction determines suitable plots, summary statistics, and models for the variable.

Common probability distributions match different data-generating processes.

• The binomial distribution models successes in a fixed number of trials, such as conversions among one thousand visitors.
• The Poisson distribution models event counts per interval, such as support tickets per hour, and is useful for rare events.
• The exponential distribution models waiting time between events, such as time until the next failure.
• The normal distribution models sums and averages of many small effects or measurement noise, but using it for heavy-tailed money data produces systematically wrong conclusions.