Pearson International GCSE Mathematics A 4: Statistics

Statistics turns collected data into summaries, comparisons and probability-based decisions.

Pearson 4MA1 Statistics requires attention to how data were obtained as well as how they are processed. A precise average from a biased sample is not representative, and a polished diagram can mislead if it uses the wrong scale, density or event model.

Main ideas

• Distinguish populations, samples, discrete data and continuous data.
• Calculate and interpret averages and measures of spread.
• Construct and interpret frequency tables, histograms, cumulative-frequency diagrams, box plots and scatter graphs.
• Estimate statistics from grouped data and explain limitations of estimates.
• Use probability scales, sample spaces, tree diagrams and set notation.
• Apply addition and multiplication rules with attention to exclusivity and independence.

Population, sample and data type

The population is the complete group of interest; a sample is the subset observed. A census studies every member but can be expensive or impractical. A sample can estimate population behaviour only when selection and non-response do not create serious bias.

Simple random sampling gives each member an equal selection opportunity. Systematic sampling uses every kth member after a suitable start. Stratified sampling represents defined subgroups in population proportions. Convenience and voluntary-response samples are easy to collect but often biased.

Categorical data describe groups. Numerical data may be discrete counts or continuous measurements. Data type determines valid summaries and diagrams. A category code such as 1 for red and 2 for blue does not make colour numerical.

Averages and spread

The mean uses every value and is sensitive to extremes. The median is the middle after ordering and resists outliers. The mode is the most frequent value or category. Choose an average by context rather than assuming the mean is always best.

Range is maximum minus minimum. Interquartile range measures the spread of the middle half and pairs naturally with the median. Two data sets with the same mean can have very different spread, so comparisons should discuss both centre and variability.

For a frequency table, multiply each value by frequency before summing and divide by total frequency. For grouped continuous data, use class midpoints, making the result an estimate because exact values within each class are unknown.

Frequency diagrams and histograms