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11 January 2024

Statistics 5.5. The normal distribution

(9709) CIE A Level Maths 2023 - 2025

1. Revision notes


Key concepts
  1. Continuous random variables: Infinite number of possible outcomes
    • histograms
      • area under curve = 1
    • normal curve: bell shaped, symmetrical
      • mean = median = mode
  2. The normal distribution:
    • The standard normal variable Z
    • Critical values table
    • Standardizing a normal distribution
    • Modeling in real-life situations
  3. Normal approximation to the binomial distribution
    • continuity correction: used when we approximate a discrete distribution by a continuous distribution

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10 January 2024

Statistics 5.4.2. Discrete random variables: The binomial and geometric distributions

(9709) CIE A Level Maths 2023 - 2025

1. Revision notes


Key concepts
  1. The binomial distribution: In a fixed number of trials, how many successes are there?
  2. The geometric distribution: In an infinite number of trials, what is the probability of the first successful trial?
  3. Variance Var(X) and expectation/mean E(X)

09 January 2024

Statistics 5.4.1. Discrete random variables: Probability distribution

(9709) CIE A Level Maths 2023 - 2025

1. Revision notes


Key concepts
  1. discrete random variables
  2. expected outcome / expectation: E(X), a.k.a. the mean
  3. variance: Var(X) - the spread of values around the mean

08 January 2024

Statistics 5.3. Probability

(9709) CIE A Level Maths 2023 - 2025

1. Revision notes


Key concepts
  1. addition and multiplication of probabilities
  2. exclusive events: events that canNOT occur at the same time
  3. independent events: one event occurs and has NO affect on the other, regardless of whether the second occurs or not
    • determining independent and dependent events
  4. conditional probabilities

06 January 2024

Statistics 5.2. Permutations and Combinations

(9709) CIE A Level Maths 2023 - 2025

1. Revision notes


Key concepts
  1. permutations: order/ arrangement matters
  2. combinations: order/ arrangement DOESN'T matter
  3. arrangements of objects
    • with repetition
    • with restriction

Statistics 5.1.3. Measures of Variation

(9709) CIE A Level Maths 2023 - 2025

1. Revision notes


Key concepts
  1. range, interquartile range
  2. cumulative frequency graphs
  3. box-and-whisker diagrams
  4. variance and standard deviation
    • grouped data
    • ungrouped data
  5. coded data