---
title: "Absolute vs relative dispersion; horses"
subject: "Probability and Statistics"
chapter: 1
key: "semester_5/probability_and_statistics:horses-consistency-dispersion"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/horses-consistency-dispersion
site: BCT Engineering
---

# Absolute vs relative dispersion; horses

Probability and Statistics · Chapter 1: Descriptive Statistics and Basic Probability

- Asked in: 2076 Asoj, 5 marks
- Video: [Absolute and relative measures of dispersion ch 4 lec 10](https://www.youtube.com/watch?v=OSXYsUjxGsM) — Naz Academy
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/horses-consistency-dispersion
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1

## Question

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 |

## 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.

## Answer

#### 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

```text
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

```text
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does a relative measure differ from an absolute one?
   A. It is in data units
   B. It is unit-free (ratio or %), so suits comparing different means
   C. It is just the range
   D. It cannot compare sets
   Answer: B. Relative measures like CV compare variability across sets. (Key point: Absolute vs relative)

2. Why is CV used for the horses?
   A. The data are qualitative
   B. The sets have different sizes
   C. The two horses have different means
   D. The data have outliers
   Answer: C. Different means make SDs not directly comparable. (Key point: Which to use)

3. Which horse is more consistent?
   A. Horse A, CV 6.93%
   B. Horse A, larger SD
   C. They are equal
   D. Horse B, CV 2.35% vs 6.93%
   Answer: D. Smaller CV means more consistent. (Key point: Result)

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