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WST01 Statistics 1

Edexcel IAL Mathematics, S1 (AS unit, usually Year 12). 30 lessons so far, in the suggested order.

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Lessons in WST01

  1. Expectation of a discrete random variable
    E(X) = sum xP(X = x); Var(X) = E(X2) - E(X)2; E(aX + b) = aE(X) + b; Var(aX + b) = a2 Var(X).
  2. Mathematical models in statistics
    Model, predict, collect data, compare, refine. Models are simplified, cheap and predictive, but never perfect.
  3. Stem-and-leaf diagrams
    Always use the key. Quartiles: n/4 not whole means round up; whole means average that value and the next. Compare location and spread, in context.
  4. Histograms and frequency density
    Frequency density = frequency ÷ class width; area is proportional to frequency; use one bar to fix the scale.
  5. Box plots and comparing distributions
    Box from Q1 to Q3 with the median; whiskers to the extreme non-outliers; compare median and IQR in context.
  6. Mean, median and mode
    x̄ = Σx/n or Σfx/Σf; median is not affected by outliers; combine groups using totals.
  7. Grouped data: estimating the mean and median
    Estimated mean = Σfx/Σf with midpoints; median = L + (n/2 - cf before)/f × width.
  8. Quartiles, percentiles and interpercentile ranges
    IQR = Q3 - Q1 (middle 50%); P90 - P10 (middle 80%); interpolate at P/100 × n for grouped data.
  9. Variance and standard deviation
    σ2 = Σx2/n - x̄2 = Sxx/n, with frequencies σ2 = Σfx2/Σf - x̄2. Keep the exact mean.
  10. Coding
    y = (x - a)/b gives x̄ = bȳ + a and σx = bσy. Shifts do not change spread.
  11. Skewness
    Compare Q3 - Q2 with Q2 - Q1, or the mean with the median. Bigger upper gap or mean > median: positive skew.
  12. Outliers and cleaning data
    Use the rule in the question; remove errors, keep genuine values; recalculate from adjusted Σx and Σx2.
  13. Sample spaces and elementary probability
    List the sample space; P(A) = favourable ÷ total for equally likely outcomes; P(A') = 1 - P(A).
  14. Venn diagrams and the addition rule
    P(A ∪ B) = P(A) + P(B) - P(A ∩ B); mutually exclusive means P(A ∩ B) = 0; fill Venn diagrams from the centre out.
  15. Conditional probability
    P(A | B) = P(A ∩ B)/P(B). The denominator is always the 'given' event.
  16. Independent events
    Independent: P(A ∩ B) = P(A)P(B). Mutually exclusive: P(A ∩ B) = 0. Show the numbers when testing.
  17. Tree diagrams, with and without replacement
    Multiply along branches, add between paths; without replacement, change the second-stage fractions.
  18. Scatter diagrams and types of variable
    Explanatory on x, response on y; describe direction and strength; correlation is not causation.
  19. Sxx, Sxy and the product moment correlation coefficient
    r = Sxy/sqrt(SxxSyy); between -1 and 1; interpret in context; unaffected by linear coding.
  20. The least squares regression line
    b = Sxy/Sxx, a = ȳ - bx̄; the line passes through (x̄, ȳ); interpret b as the rate of change in context.
  21. Using regression lines: prediction and coding
    Interpolate, do not extrapolate; check predictions make sense; for coded lines, substitute the codes and rearrange.
  22. Discrete random variables and probability functions
    p(x) = P(X = x); the probabilities sum to 1; read < and ≤ carefully.
  23. The cumulative distribution function
    F(x) = P(X ≤ x); P(X = x) = F(x) - F(x - 1); F(max) = 1, not ΣF = 1.
  24. Variance, unknown probabilities and functions of X
    Use ΣP = 1 and E(X) to find two unknowns; E(g(X)) = Σg(x)P(X = x); Var(aX + b) = a2Var(X).
  25. The discrete uniform distribution
    Uniform on 1 to n: E = (n + 1)/2, Var = (n2 - 1)/12; otherwise rewrite as aX + b.
  26. The normal distribution and the standard normal table
    Z = (X - μ)/σ; Φ(z) = P(Z < z); use 1 - Φ and symmetry for other areas; always sketch.
  27. Normal probabilities in context
    Standardise, sketch, use the table and symmetry; expected number = n × p; P(A | B) = P(A)/P(B) when A is inside B.
  28. Inverse normal: finding values from probabilities
    Sketch, find z from the percentage points table (4 d.p.), use x = μ + zσ; z is negative below the mean.
  29. Finding an unknown mean or standard deviation
    Standardise with the table z (4 d.p.) and solve for μ or σ; two probabilities give simultaneous equations.
  30. S1 exam technique
    3 s.f. unless told; exact values in working; z to 4 d.p.; show every step; interpret in context; sanity-check answers.

Next exams for WST01

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