Statistics Study Guide for Data Science Interviews

Measures of Central Tendency

Mean, Median, Mode

Mean

Average value, sensitive to outliers

Median

Middle value when data is ordered; robust to outliers

Mode

Most frequently occurring value

When to use mean, median, and mode

Mean for normal distributions, median for skewed data, mode for categorical data

Measures of Variability

Variance, Standard Deviation, Range, Interquartile Range (IQR)

Variance

Average of squared deviations from mean

Standard Deviation

Square root of variance; same units as original data

Range

Difference between max and min values

Interquartile Range (IQR)

Range of middle 50% of data; robust to outliers

Skewness

Measure of asymmetry (positive = right tail, negative left tail)

Kurtosis

Measure of tail heaviness compared to normal distribution

Addition Rule

P(A or B) = P(A) + P(B) - P(A and B)

Multiplication Rule

P(A and B) = P(A) * P(B|A)

Conditional Probability

P(A|B) = P(A and B)/P(B)

Bayes’ Theorem

Formula: P(A|B) = P(B|A) * P(A)/P(B)

Key concept: Updates prior probability with new evidence

Common interview trap: Confusing P(A|B) with P(B|A)

Independent Events

P(A|B) = P(A); knowing B doesn’t change probability of A

Mutually Exclusive

P(A and B) = 0; events cannot occur together

Independence vs. Mutual Exclusivity Common Mistake

Assuming mutually exclusive events are independent

Normal Distribution Properties

Bell-shaped, symmetric, defined by mean and standard deviation

68-95-99.7 Rule

~68% within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD

Standard Normal

Mean = 0, SD = 1; used for z-scores

Central Limit Theorem (CLT)

Key insight: Sample means approach normal distribution as sample size increases

Rule of thumb: n >= 30 for CLT to apply

Why it matters: Enables inference even when population isn’t normal

Binomial Distribution

Number of successes in fixed number of trials

Poisson Distribution

Count of rare events in fixed time/space

Exponential Distribution

Time between events in Poisson process

t-distribution

Used when sample size is small and population SD unknown

Hypothesis Testing Core Framework

1. Null Hypothesis (H0): Status quo assumption

2. Alternative Hypothesis (H1): What we’re trying to prove

3. Test Statistic: Standardized measure of evidence against H0

4. p-value: Probability of observing data this extreme if H0 is true

5. Decision: Reject H0 if p-value < alpha (significance level)

Type I Error (alpha)

Rejecting true null hypothesis (false positive)

Type II Error (beta)

Failing to reject false null hypothesis (false negative)

Power

1 - beta; probability of correctly rejecting false null hypothesis

Trade-off

Decreasing alpha increases beta, and vice versa

One-sample t-test

Compare sample mean to known value

Two-sample t-test

Compare means of two groups

Paired t-test

Compare before/after measurements

Chi-square test

Test independence between categorical variables

ANOVA (Analysis of Variance)

Compare means across multiple groups

p-hacking

Manipulating analysis to achieve significant p-value

Multiple testing problem

Increased chance of Type I error with multiple tests

Bonferroni correction

Adjust alpha by dividing by number of tests

Confidence Interval Interpretation

CORRECT: “We are 95% confident the interval contains the true parameter.”

INCORRECT: “There’s a 95% chance the parameter is in this interval.”

KEY POINT: The interval is random, NOT the parameter.

Factors Affecting Width (of confidence interval)

• Sample size: Larger n → narrower interval

• Confidence level: Higher confidence → wider interval

• Population variability → wider interval

Pearson Correlation

Linear relationship between continuous variables (-1 to +1)

KEY LIMITATION: Only captures linear relationships

Spearman Correlation

Monotonic relationship; uses ranks

Requirements for establishing causation

• Temporal precedence

• Covariation

• No confounding variables

Common fallacy of causation

Assuming correlation implies causation

Solutions for establishing causation

• Randomized experiments

• Instrumental variables

• Natural experiments

Types of Sampling Bias

• Selection Bias

• Survivorship Bias

• Response Bias

• Confirmation Bias

Selection Bias

Non-representative sample selection

Survivorship Bias

Only analyzing “survivors” of a process

Response Bias

Systematic differences in who responds

Confirmation Bias

Seeking data that confirms preconceptions

Factors of Sample Size Determination

• Desired confidence level

• Margin of error

• Population variability

Power analysis for sample size determination

Determining sample size needed to detect meaningful effect

Common mistake in sample size determination

Use sample size formulas without considering effect size

A/B Testing Design Principles

• Randomization

• Power calculation

• Duration

• Primary metric

Randomization

Ensures groups are comparable

Power calculation

Determine sample size before starting

Duration

Balance statistical power with external validity

Primary metric

Define success metric before starting

A/B Testing Common Pitfalls

• Peeking

• Novelty effect

• Simpson’s paradox

Peeking

Checking results before predetermined end

Novelty effect

Initial behavior change due to change itself

Simpson’s paradox

Trend reverses when data is segmented