Statistical Analysis: Data, Spread and Bivariate Relationships
What you must understand
Statistical analysis requires summarising data and interpreting what the summaries mean. Know how to classify data as categorical or numerical, and how to display it appropriately. You must calculate and interpret the mean, median, mode, range, interquartile range and standard deviation, and understand that the standard deviation measures spread about the mean. You should be able to read and construct box plots and histograms, identify outliers, and describe shape (symmetric or skewed). For bivariate data, you need scatterplots, correlation (strength and direction), the least-squares line of best fit, and interpolation versus extrapolation.
Traps to watch
- Median with an even number of values: average the two middle values.
- Quartiles: with small data sets, methods differ; follow the method used in your course and be consistent.
- Standard deviation: it is never negative, and a larger value means greater spread, not a larger mean.
- Correlation is not causation: a strong correlation does not prove one variable causes the other.
- Extrapolation: predicting well outside the data range is unreliable.
- Outliers: they affect the mean much more than the median.
Worked example
Data: 4, 6, 7, 9, 14. Mean = 40 ÷ 5 = 8. Median = 7. The value 14 is far above the rest, so the distribution is positively skewed and the mean exceeds the median.
Rule of thumb
Always describe a distribution with centre, spread, shape and outliers. When comparing two data sets, compare both a measure of centre and a measure of spread.