Explain range and standard deviation with their merits and demerits. Add a worked example.

1. 1 · Define dispersion. Dispersion is the spread of values around the average. Two groups can have the same mean but very different spread.
2. 2 · Range. R = L − S; coefficient of range = (L − S) ÷ (L + S). Merits: simple and quick. Demerits: uses only two values, upset by extremes.
3. 3 · Standard deviation. σ = √[Σ(x − x̄)² ÷ n]. Note that the sample SD divides by n − 1.
4. 4 · Merits and demerits of SD.
   • Merits: uses all values, rigidly defined, stable from sample to sample, basis for correlation and the t test.
   • Demerits: harder to calculate; squaring gives extra weight to extreme values.
5. 5 · Work an example. [Deviation table: x, x − x̄, (x − x̄)², with column totals]
6. 6 · Nutrition link. Results are written as mean ± SD; a large SD shows wide variation in intake within the group.
7. 7 · Close in one line. SD is the most reliable measure of dispersion; range is only a quick first look.

Scoring tip: Draw the deviation table with column totals, and check that Σ(x − x̄) = 0 before you square.