Explain Karl Pearson's coefficient of correlation. State its merits and demerits.

1. 1 · Define correlation and its types. Correlation is the degree to which two variables change together. Karl Pearson's r measures linear correlation.
   • Positive: both move in the same direction.
   • Negative: they move in opposite directions.
   • Zero: no linear link.
2. 2 · Formula. r = Σdxdy ÷ √(Σdx² × Σdy²), with dx = x − x̄ and dy = y − ȳ.
3. 3 · Interpretation. r lies between −1 and +1. The sign shows direction; the size shows strength (high, moderate, low).
4. 4 · Scatter diagrams. [Sketch three scatter plots: positive, negative and no correlation]
5. 5 · Worked example. Solve a 5-pair sum, such as exercise hours and BMI, with a deviation table.
6. 6 · Merits and demerits.
   • Merits: direction and strength in one number, uses all pairs, has no units.
   • Demerits: linear links only, affected by outliers, does not prove cause.
7. 7 · Nutrition link. Used for links such as sodium intake and blood pressure; association is not causation.
8. 8 · Close in one line. r is the most widely used measure of correlation, but it must be read with care.

Scoring tip: The scatter sketches and one correct sum carry most of the marks. Always interpret your r in words.