Statistics

GCSE Statistics includes qualitative and quantitative data, where qualitative data describes categories or qualities and quantitative data records numerical values that can be measured or counted.

Quantitative data can be discrete or continuous; discrete data takes separate countable values, while continuous data can take any value within an interval, such as height, mass, time or temperature.

The distinction between independent and dependent variables is important in statistical investigations: the independent variable is the factor that is changed or used to explain variation, while the dependent variable is the measured outcome.

Population and sample are different statistical ideas; a population is the full group being studied, while a sample is a smaller group selected from that population to make conclusions about the whole.

A good sample should be representative, sufficiently large and unbiased, because a poor sampling method can produce misleading results that do not reflect the population accurately.

Primary data is collected directly for a particular investigation, while secondary data comes from information that has already been collected by another source, such as government statistics or published research.

The mean is calculated using $\frac{\text{sum of all values}}{\text{number of values}}$, while the median is the middle ordered value, so median vs mean questions often test which average is more suitable for the data.

The mode is the most frequently occurring value and the range is calculated using $\text{maximum value}-\text{minimum value}$, giving a simple measure of how spread out the data is.

An outlier is a value that is unusually far from the rest of the data and can affect the mean, range and overall interpretation of a distribution, so outliers should be identified and considered when drawing conclusions.

Frequency tables organise data into values or groups and show how often each occurs, while grouped frequency tables can be used to estimate averages when the exact individual values are not known.

Pie charts represent proportions of a total, with each sector angle calculated using $\frac{\text{frequency}}{\text{total frequency}}\times360^\circ$, while bar charts and line graphs are used for other forms of categorical, discrete and time-series data.

Scatter graphs are used to compare two numerical variables and identify positive correlation, negative correlation or no correlation, while a stronger relationship is shown when points lie more closely around a clear pattern.

A line of best fit, also called a best fitted line or best fit line, is drawn through the trend in a scatter graph and can be used to estimate values, make predictions and compare relationships between variables.

Correlation vs causation is a key statistics concept: correlation shows that two variables are associated, but it does not prove cause and effect, because another variable may influence both or the relationship may be coincidental.

GCSE statistics questions and GCSE statistics past papers commonly test data types, sampling, median vs mean, outliers, charts, pie chart calculations, scatter graphs, correlation vs causation, lines of best fit, interpolation, extrapolation and whether conclusions are justified by the evidence.