What are mean, median, and mode? — Mean: Sum of values ÷ number of values (average). Median: Middle value when sorted (or average of two middle values if even count). Mode: Most frequently occurring value.
What is range and interquartile range (IQR)? — Range: Maximum − Minimum. IQR: Q3 − Q1 (middle 50% of data). IQR is resistant to outliers, making it more reliable than range for skewed data.
What is standard deviation (σ or s)? — A measure of how spread out data is from the mean. Population σ = √(Σ(x−μ)²/N). Sample s = √(Σ(x−x̄)²/(n−1)). Larger SD = more spread out.
What is variance? — The square of the standard deviation. σ² (population) or s² (sample). Variance is in squared units; standard deviation brings it back to the original units.
What is a box plot (box and whisker plot)? — A visual summary showing: minimum, Q1, median (Q2), Q3, maximum. The box spans Q1 to Q3 (IQR). Whiskers extend to min/max (or 1.5×IQR for outlier detection).
What is the empirical rule (68-95-99.7 rule)? — In a normal distribution: 68% of data falls within 1 SD of the mean. 95% within 2 SDs. 99.7% within 3 SDs.
What is a z-score and its formula? — z = (x − μ) / σ. It tells how many standard deviations x is from the mean. z=0 means at the mean. z=2 means 2 SDs above. Used to standardize and compare values.
What is the normal distribution? — A symmetric, bell-shaped distribution defined by its mean (μ) and standard deviation (σ). The mean = median = mode. Described by: f(x) = (1/σ√2π) e^(−½((x−μ)/σ)²).
What is probability and how is it measured? — The likelihood of an event occurring. P(event) = favorable outcomes / total possible outcomes. Always between 0 (impossible) and 1 (certain).
What is the addition rule for probability? — P(A or B) = P(A) + P(B) − P(A and B). For mutually exclusive events (cannot both occur): P(A or B) = P(A) + P(B).
What are permutations and their formula? — Arrangements where order matters. P(n,r) = n! / (n−r)! — number of ways to arrange r items from n distinct items. Example: arranging 3 from 5 = 5!/2! = 60.
What are combinations and their formula? — Selections where order does NOT matter. C(n,r) = n! / (r!(n−r)!) — also written as ⁿCᵣ or (n r). Example: choosing 3 from 5 = 10.
What is a binomial distribution? — Models the number of successes in n independent trials, each with probability p of success. P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. Mean = np. Variance = np(1−p).
What is a Poisson distribution? — Models the number of events in a fixed interval when events occur at a constant mean rate λ. P(X=k) = (e⁻λ × λᵏ) / k!. Mean = λ. Variance = λ. Used for rare events.
What is the Central Limit Theorem (CLT)? — If samples of size n are drawn from any population with mean μ and SD σ, the distribution of sample means approaches a normal distribution as n increases. Typically, n ≥ 30 is sufficient.
What is a confidence interval? — A range of values that is likely to contain the true population parameter with a given confidence level. Example: 95% CI for a mean: x̄ ± z × (σ/√n).
What is hypothesis testing? — A procedure to test a claim about a population parameter. Steps: 1. State H₀ (null) and H₁ (alternative). 2. Choose significance level α. 3. Calculate test statistic. 4. Find p-value. 5. Reject H₀ if p < α.
What is a p-value? — The probability of observing results at least as extreme as the sample data, assuming H₀ is true. p < α (usually 0.05) → reject H₀. p ≥ α → fail to reject H₀.
What is Type I and Type II error? — Type I (α): Rejecting H₀ when it is actually true (false positive). Type II (β): Failing to reject H₀ when it is actually false (false negative). Power = 1 − β.
What is correlation (r) and what does it measure? — A measure of the linear relationship between two variables. r = +1: perfect positive correlation. r = −1: perfect negative correlation. r = 0: no linear correlation.
What is the difference between correlation and causation? — Correlation means two variables tend to change together. Causation means one variable directly causes the other. Correlation does not imply causation — there may be confounding variables.
What is linear regression and its equation? — A method to model the relationship between two variables with a straight line: ŷ = a + bx where b = slope and a = y-intercept. The least squares line minimizes the sum of squared residuals.
