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Intro Statistics — Descriptive Statistics and Probability flashcards

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The first half of a college intro statistics course: data types and sampling, graphs, center and spread, z-scores, probability rules and conditional probability, binomial, Poisson and other discrete models, uniform and exponential models, and the normal distribution.

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Learn deck · part of Introductory Statistics · written against: Standard one-semester intro statistics course; OpenStax Introductory Statistics 2e, consulted as a reference; no text copied. Updated 2026-10-10.

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  1. A survey records how many siblings each student has. Is that variable discrete or continuous?
    Discrete quantitative. Counts can only take separate values (0, 1, 2, …), with nothing in between.

    Watch out: quantitative does not mean continuous — continuous variables are measurements such as height or time.
    Sampling and Data
  2. What are the four levels of measurement, from least to most informative?
    Nominal (categories only), ordinal (categories with an order), interval (equal differences but no true zero) and ratio (a true zero, so ratios make sense).

    Example: blood type, class rank, temperature in °C, weight in kg.
    Sampling and Data
  3. A bar chart comparing two companies' satisfaction scores starts its vertical axis at 95 instead of 0. Why can that mislead?
    Diagram that comes with this cardA truncated axis stretches small differences: a gap of 96 vs. 98 can look like one bar is several times taller. Check the axis scale before judging the size of a difference.
    Descriptive Statistics › Graphs
  4. Using the median-of-halves method, what are the quartiles and IQR of 1, 3, 4, 6, 7, 8, 10, 12?
    Diagram that comes with this cardLower half 1, 3, 4, 6 gives Q1 = 3.5; upper half 7, 8, 10, 12 gives Q3 = 9; so IQR = 5.5.

    Watch out: software packages use slightly different quartile rules, so small differences from a textbook answer are normal.
    Descriptive Statistics › Center and Spread
  5. One card is drawn from a standard deck. What is P(heart or king)?
    Diagram that comes with this cardThe events overlap (the king of hearts), so use the general addition rule: 1352+452−152=1652≈0.308\frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52} \approx 0.308⁠.
    Probability Topics
  6. At a college, 60% of students take statistics, 50% take economics and 30% take both. What share take neither?
    Diagram that comes with this cardP(stats or econ) = 0.60 + 0.50 − 0.30 = 0.80, so P(neither) = 1 − 0.80 = 0.20. A Venn diagram makes the overlap easy to see.
    Probability Topics
  7. X takes the values 0, 1 and 2 with probabilities 0.2, 0.5 and 0.3. What are its mean and standard deviation?
    μ=0(0.2)+1(0.5)+2(0.3)=1.1\mu = 0(0.2) + 1(0.5) + 2(0.3) = 1.1⁠. Then σ2=∑(x−μ)2p=0.49\sigma^2 = \sum (x - \mu)^2 p = 0.49⁠, so σ=0.7\sigma = 0.7⁠.
    Discrete Random Variables › Expected Value
  8. How does the shape of a binomial distribution depend on p and n?
    Diagram that comes with this cardIt is symmetric when p = 0.5, right-skewed when p is small and left-skewed when p is large. As n grows, the skew fades and the distribution becomes more bell-shaped.
    Discrete Random Variables › Binomial
  9. A shuttle arrives at a uniformly random time within a 20-minute window. What is the probability you wait more than 15 minutes?
    Diagram that comes with this cardFor a uniform distribution, probability is proportional to length: 20−1520=0.25\frac{20 - 15}{20} = 0.25⁠.
    Continuous Random Variables
  10. A test is normal with mean 500 and SD 100. By the empirical rule, roughly what share of test-takers score between 400 and 700?
    Diagram that comes with this cardFrom −1 to +2 SDs: 34% + 34% + 13.5% = 81.5%. Exact normal tables give about 81.9%.
    The Normal Distribution

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About these cards

Review status: Second-reader reviewed, with corrections applied.

Checked against:

  • OpenStax Introductory Statistics 2e, consulted as a reference; no text copied.
  • Diagrams are original, drawn for this deck by tools/diagrams/intro_statistics.py from the numbers on each card (SVG source and PNG in media/).

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