- 2076 Asoj · 5 marks
Absolute vs relative dispersion; horses
Short answer
Horse B is more consistent because its coefficient of variation (2.35%) is much smaller than Horse A’s (6.93%). Means and SD differ; use CV for comparison. Horse A: mean 278.33, SD 19.29; Horse B: mean 290, SD 6.81.
Distinguish between absolute and relative measures of dispersion. The running capacity of two horses is given below, state which is more consistent and why?
| Horse A | 250 | 255 | 280 | 290 | 295 | 300 |
|---|---|---|---|---|---|---|
| Horse B | 280 | 282 | 290 | 295 | 298 | 295 |
Absolute and relative measures of dispersion
| Basis | Absolute measure | Relative measure |
|---|---|---|
| Meaning | Spread in the units of the data | Spread as a ratio or percentage, free of units |
| Examples | Range, quartile deviation, mean deviation, standard deviation | Coefficient of range, coefficient of quartile deviation, coefficient of variation |
| Use | One data set at a time | Comparing two sets with different units or different means |
Horses: which is more consistent?
Because the two horses have different means, compare them using the coefficient of variation (CV = σ / x̄ × 100). The six readings of each horse are taken as the full data (divisor n).
Horse A: Σx = 1670, mean = 278.33
Σ(x − x̄)² = 2233.3, σ² = 372.2, σ = 19.29
CV = 19.29 / 278.33 × 100 = 6.93 %
Horse B: Σx = 1740, mean = 290
Σ(x − x̄)² = 278.0, σ² = 46.33, σ = 6.81
CV = 6.81 / 290 × 100 = 2.35 %
| Mean | SD | CV | |
|---|---|---|---|
| Horse A | 278.33 | 19.29 | 6.93 % |
| Horse B | 290 | 6.81 | 2.35 % |
Answer: Horse B is more consistent because its CV (2.35 %) is much smaller than that of Horse A (6.93 %). Horse B also has the higher average.
✓ Answer checked by Claude Sonnet 5.5
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