← Further Maths syllabus

EnglandFurther Maths

Further Statistics (optional)

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you test whether data fit a distribution or whether two factors are independent, and what non-parametric tests are available?

The chi-squared goodness-of-fit test and contingency table test for independence, degrees of freedom, and non-parametric tests including the sign test and Wilcoxon signed-rank test.
A focused answer to the OCR A-Level Further Mathematics A Statistics option content on chi-squared and non-parametric tests, covering the chi-squared goodness-of-fit test and the contingency table test for independence with their degrees of freedom and expected frequencies, and non-parametric tests including the sign test and the Wilcoxon signed-rank test.
12 min answer →

How do you work with a continuous random variable defined by a probability density function?

Continuous random variables, the probability density function and cumulative distribution function, finding probabilities by integration, and the expectation and variance of a continuous variable.
A focused answer to the OCR A-Level Further Mathematics A Statistics option content on continuous random variables, covering the probability density function and the condition that it integrates to one, finding probabilities by integration, the cumulative distribution function and its relationship to the pdf, and the expectation and variance of a continuous variable.
12 min answer →

How do you describe a discrete random variable and find its expectation and variance?

Discrete random variables, the probability distribution, expectation and variance, and the effect of a linear transformation aX + b on the mean and variance.
A focused answer to the OCR A-Level Further Mathematics A Statistics option content on discrete random variables, covering the probability distribution and the condition that probabilities sum to one, the expectation E(X) and variance Var(X), the computational formula for variance, and the effect of a linear transformation aX plus b on the mean and variance.
11 min answer →

How do the Poisson and geometric distributions model counts and waiting times, and when does each apply?

The Poisson distribution and its conditions, mean and variance, the sum of independent Poisson variables, the geometric distribution and its mean, and the Poisson approximation to the binomial.
A focused answer to the OCR A-Level Further Mathematics A Statistics option content on the Poisson and geometric distributions, covering the Poisson model and its conditions, its mean and variance both equal to lambda, the sum of independent Poisson variables, the geometric distribution for the number of trials to the first success and its mean, and the Poisson approximation to the binomial.
12 min answer →