Master statistics and probability with this comprehensive flashcard deck covering every key concept from descriptive statistics to inferential analysis. Statistics is increasingly essential in every field — from medicine and economics to machine learning and s...
Master statistics and probability with this comprehensive flashcard deck covering every key concept from descriptive statistics to inferential analysis. Statistics is increasingly essential in every field — from medicine and economics to machine learning and social sciences — and it is a major component of AP Statistics, A-Level Mathematics, IB Mathematics, and undergraduate courses.
This deck covers measures of central tendency and spread, probability rules, permutations and combinations, discrete and continuous probability distributions (including the normal distribution), hypothesis testing, confidence intervals, correlation and regression,
and the central limit theorem. Based on publicly available resources including OpenStax Statistics and Khan Academy.
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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.
Range: Maximum − Minimum. IQR: Q3 − Q1 (middle 50% of data). IQR is resistant to outliers, making it more reliable than range for skewed data.
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.
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.
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).
In a normal distribution: 68% of data falls within 1 SD of the mean. 95% within 2 SDs. 99.7% within 3 SDs.
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.
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).
The likelihood of an event occurring. P(event) = favorable outcomes / total possible outcomes. Always between 0 (impossible) and 1 (certain).
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).
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.
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.
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).
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.
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.
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).
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.
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.
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.
A measure of the linear relationship between two variables. r = +1: perfect positive correlation. r = −1: perfect negative correlation. r = 0: no linear correlation.
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.
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.
