GCSE / Maths
Probability
Revise GCSE Maths Probability, including experimental and theoretical probability, relative frequency, expected frequency, sample spaces, Venn diagrams, tree diagrams, independent and dependent events, mutually exclusive events and conditional probability.
GCSE Statistics focuses on collecting, organising, representing, analysing and interpreting data, including averages, frequency tables, charts, sampling, scatter graphs, correlation and conclusions drawn from statistical evidence.
Statistical data can be discrete or continuous; discrete data takes separate countable values such as the number of students, while continuous data can take any value within a range such as height, mass or time.
An independent variable is the variable that is changed, controlled or used to explain variation, while a dependent variable is the measured outcome that may change in response to the independent variable.
The mean is calculated using , while the median is the middle value when the data is placed in order, so median vs mean questions test which average is more suitable for a particular data set.
The median is often more appropriate than the mean when data contains extreme values or outliers because the mean can be pulled significantly up or down by unusually large or small values.
Frequency tables organise data by recording how often each value or category occurs, making it easier to calculate totals, compare groups and identify patterns in the distribution.
For grouped frequency data, an estimate of the mean is calculated using , where is the midpoint of each class interval and is the corresponding frequency, so the answer is an estimate rather than an exact mean.
A population is the complete group being studied, while a sample is a smaller group selected from that population, and the quality of a statistical conclusion depends on whether the sample is sufficiently large, random and representative.
Sample size affects reliability because larger representative samples usually reduce the effect of random variation, while a small or biased sample can give misleading results that do not reflect the population accurately.
Pie charts represent categorical data using sectors of a circle, and each sector angle is calculated using , so a larger frequency produces a larger sector.
Bar charts, frequency diagrams, line graphs and pie charts should use suitable scales, clear labels, correct units and accurate plotting because poor presentation can make statistical information difficult or misleading to interpret.
Scatter graphs are used to investigate the relationship between two variables and can show positive correlation, negative correlation or no correlation depending on the overall pattern of the plotted points.
Correlation vs causation is a key GCSE Statistics idea because correlation shows that two variables are related, but it does not prove that one variable causes the other, as a third factor may influence both variables.
A line of best fit summarises the trend in a scatter graph and can be used to estimate values, but interpolation within the observed data range is generally more reliable than extrapolation far beyond the existing data.
GCSE statistics past papers commonly assess mean, median, frequency tables, grouped data, sample size, independent vs dependent variable, discrete vs continuous data, pie charts, scatter graphs, correlation vs causation and whether a conclusion is justified by the evidence.