A survey records household income only in the classes £0–£20 000, £20 000–£40 000, £40 000–£60 000 and “£60 000 or more”. The researcher uses £70 000 as the midpoint of the final class.
Explain why the resulting estimated mean is especially model-dependent.
Explain why the median may be a more stable summary for these data.
Suggest a refinement that would allow a more defensible estimate of the mean.
121 exam-style questions on OCR (MEI) A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Types of data and standard diagrams, 2.2.2 Area in a histogram is proportional to frequency, 2.2.3 Cumulative frequency diagram, 2.2.4 Describe frequency distributions, 2.2.5 Samples and theoretical distributions, 2.2.6 Interpret a scatter diagram, 2.2.7 Distinct sections and outliers in scatter diagrams, 2.2.8 Correlation and causation, 2.2.9 Select or critique data presentation techniques, 2.2.10 Measures of central tendency, 2.2.11 Simple measures of spread, 2.2.12 Variance and standard deviation, 2.2.13 Outliers, 2.2.14 Cleaning data, and 2.2 Data Presentation and Interpretation. Each one has a worked solution and a mark scheme showing where the marks go.