Mathematics 9709 — specification explorer

1. Representation of data

• 5.1.1select a suitable way of presenting raw statistical data, and discuss advantages and/or disadvantages that particular representations may have
• 5.1.2draw and interpret stem-and-leaf diagrams, box- and-whisker plots, histograms and cumulative frequency graphs
• 5.1.3understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation)
• 5.1.4use a cumulative frequency graph
• 5.1.5calculate and use the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals ∑x and ∑x², or coded totals ∑(x−a) and ∑(x−a)², and use such totals in solving problems which may involve up to two data sets.

2. Permutations and combinations

• 5.2.1understand the terms permutation and combination, and solve simple problems involving selections
• 5.2.2

  solve problems about arrangements of objects in Questions may include cases such as people sitting in a line, including those involving two (or more) rows. arranging the letters of the word ‘NEEDLESS’) be included. people can stand in a line if two particular people must, or must not, stand next to each other).:

  • repetition (e.g. the number of ways of Questions about objects arranged in a circle will not
  • restriction (e.g. the number of ways several

3. Probability

• 5.3.1evaluate probabilities in simple cases by means of enumeration of equiprobable elementary events, or by calculation using permutations or combinations
• 5.3.2use addition and multiplication of probabilities, as appropriate, in simple cases
• 5.3.3understand the meaning of exclusive and independent events, including determination of whether events A and B are independent by comparing the values of P(A∩B) and P(A)×P(B)
• 5.3.4calculate and use conditional probabilities in e.g. situations that can be represented by a sample simple cases. space of equiprobable elementary events, or a tree diagram. The use of

4. Discrete random variables

• 5.4.1draw up a probability distribution table relating to a given situation involving a discrete random variable X , and calculate E( X ) and Var( X )
• 5.4.2use formulae for probabilities for the binomial and geometric distributions, and recognise practical situations where these distributions are suitable models
• 5.4.3use formulae for the expectation and variance of Proofs of formulae are not required. the binomial distribution and for the expectation of the geometric distribution.

5. The normal distribution

• 5.5.1understand the use of a normal distribution to model a continuous random variable, and use normal distribution tables
• 5.5.2

  solve problems concerning a variable X , where For calculations involving standardisation, full details X + N _ n v , i , including of the working should be shown. e.g. probability, given the values of x , n , v . given the value of P _ X > x i or a related probability:

  • finding the value of P _ X > x i , or a related
  • finding a relationship between x , n and v
• 5.5.3recall conditions under which the normal distribution can be used as an approximation to the binomial distribution, and use this approximation, with a continuity correction, in solving problems.