GCSE Maths · Statistics · Foundation · Summary

GCSE Maths Statistics (Foundation): summary and key words

Chapter summary

Skill	Method
Types of data	Categorical (words), discrete (counted), continuous (measured)
Sampling	Random, unbiased sample; stratified: group ÷ population × sample size
Capture-recapture	N = marked first × second sample ÷ marked in second sample
Mean, median, mode, range	Total ÷ number; middle value in order; most common; biggest − smallest
Frequency table	Mean: total of (f × value) ÷ total f; median from running total
Grouped data	Midpoints for the estimated mean; modal class; median class
Charts	Bar chart, pictogram (use the key), pie chart (angle = f ÷ total × 360°), line graph, stem-and-leaf (with key)
Scatter graphs	Correlation, line of best fit through the mean point; interpolation is more reliable than extrapolation
Comparing	Compare an average and a spread, in context, with numbers
Quartiles (H)	Q1 and Q3 are the medians of the two halves; IQR = Q3 − Q1
Cumulative frequency (H)	Plot at the upper boundary; read n ÷ 4, n ÷ 2, 3n ÷ 4
Box plots (H)	Five numbers; box = middle half; outliers as crosses
Histograms (H)	Frequency density = frequency ÷ class width; area = frequency

I can say whether data is categorical, discrete or continuous, and design a fair question.
I can complete tally charts, frequency tables, grouped frequency tables and two-way tables.
I can spot bias, take a stratified sample and use capture–recapture.
I can find the mean, median, mode and range from lists, frequency tables and grouped tables.
I can draw and read bar charts, pictograms, pie charts, line graphs and stem-and-leaf diagrams.
I can describe correlation, draw a line of best fit and use it to estimate, knowing the dangers of extrapolating.
I can compare two distributions with an average and a spread.
Higher: I can find quartiles and the IQR, and draw and use cumulative frequency graphs and box plots.
Higher: I can draw and read histograms using frequency density.

Population: The whole group being studied.
Sample: A smaller group taken from the population.
Bias: A sample or question that unfairly favours some answers.
Stratified sample: A sample with the same proportions from each group as the population has.
Mean: The total of the values divided by how many there are.
Median: The middle value when the data is in order.
Mode: The most common value.
Range: The biggest value minus the smallest value.
Frequency: How many times a value occurs.
Modal class: The class with the highest frequency.
Correlation: How two variables are related: positive, negative or none.
Line of best fit: A straight line that follows the trend of a scatter graph.
Interpolation: Estimating inside the range of the data.
Extrapolation: Estimating outside the range of the data (less reliable).
Outlier: A value far from the rest of the data.
Quartiles: Values that split ordered data into four equal parts.
Interquartile range: Upper quartile minus lower quartile.
Cumulative frequency: A running total of the frequencies.
Frequency density: Frequency divided by class width.