Level 7: Distributions and regression

Statistics and data · level 7 of 8 · rough age 15-16 (a guide for parents; anyone can start anywhere)

In level 6 you measured spread with the standard deviation and drew lines through scatter plots by eye. In this level those ideas become exact tools. You read the shape of a distribution, model data with the normal curve, compare anything with z-scores, measure a straight-line pattern with the correlation coefficient, and find the best line by least squares, with a proof of why it is best. The level ends with curved models and with the practical work of organising and cleaning large data sets.

Lesson	You will be able to
Shapes of distributions	Describe a distribution by shape, outliers, centre and spread, and explain why a tail pulls the mean but not the median
The normal curve as a model of data	Use the 68–95–99.7 rule, explain why the bell curve appears so often, and check whether data are close to normal
z-scores and percentiles	Standardise values, compare results on different scales, and move between values, z-scores and percentiles
The correlation coefficient r	Compute r by hand, prove it lies between −1 and 1, and explain why it sees only straight-line patterns
Least-squares regression	Derive and use the least-squares line, interpret residuals, and read r² as the share of variation explained
Non-linear models	Fit exponential, quadratic and power models with technology, and choose between models with a residual plot
Organising large data sets	Store data as cases and variables, name the kind of each variable, and clean messy data with a log

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