Cambridge AS Levels Probability & Statistics 1 (Paper 5)

Select a suitable way of presenting raw statistical data, and discuss advantages and/or disadvantages that particular representations may have.

Construct and interpret stem-and-leaf diagrams, box-and-whisker plots, histograms and cumulative frequency graphs.

Understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data.

Use a cumulative frequency graph to estimate the median value, the quartiles and the interquartile range of a set of data.

Calculate the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals such as Σx and Σx², or Σ(x – a) and Σ(x – a)².

Representation of data (Part 2) - Cambridge AS Levels Probability & Statistics 1 (Paper 5) (101:57 mins)

Understand the terms permutation and combination, and solve simple problems involving selections.

• repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’)
• restriction (e.g. the number of ways several people can stand in a line if 2 particular people must — or must not — stand next to each other).

Evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events (e.g. for the total score when two fair dice are thrown), or by calculation using permutations or combinations.

Use addition and multiplication of probabilities, as appropriate, in simple cases.

Understand the meaning of exclusive and independent events, and calculate and use conditional probabilities in simple cases, e.g. situations that can be represented by means of a tree diagram.

Use formulae for probabilities for the binomial distribution, and recognise practical situations where the binomial distribution is a suitable model (the notation B(n, p) is included).

Use formulae for the expectation and variance of the binomial distribution.

Understand the use of a normal distribution to model a continuous random variable, and use normal distribution tables.

• finding the value of P(X > x₁), or a related probability, given the values of x₁, μ, σ,
• finding a relationship between x₁, μ and σ given the value of P(X > x₁) or a related probability.

Recall conditions under which the normal distribution can be used as an approximation to the binomial distribution (n large enough to ensure that np > 5 and nq > 5), and use this approximation, with a continuity correction, in solving problems.