---
title: "Interpret box plots of four plants"
subject: "Probability and Statistics"
chapter: 1
key: "semester_5/probability_and_statistics:multiple-box-plots-four-plants"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/multiple-box-plots-four-plants
site: BCT Engineering
---

# Interpret box plots of four plants

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

- Asked in: 2074 Asoj, 7 marks
- Video: [Box Plots and Quartiles - GCSE Higher Maths](https://www.youtube.com/watch?v=SUP-mBn2B2E) — 1st Class Maths
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/multiple-box-plots-four-plants
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1

## Question

The following multiple box plots show the quality index at 4 manufacturing plants. Comment on the relationships between quality at different plants and the variability present in those 4 plants.
[Figure: side-by-side box plots of quality index (vertical axis 60 to 120) for Plant 1, Plant 2, Plant 3, Plant 4. Approximate values read from the plot: Plant 1 box about 95 to 103, whiskers about 85 to 109; Plant 2 box about 82 to 100, whiskers about 65 to 118; Plant 3 box about 99 to 106, whiskers about 88 to 117; Plant 4 box about 78 to 85, whiskers about 73 to 94.]

## Short answer

Plant 3 has the highest quality and low variability, performing best. Plant 1 is also high and consistent. Plant 4 is steady but lowest. Plant 2 has moderate quality with the widest spread, making its output least predictable and in need of process improvement.

## Answer

Approximate values read from the figure (box = Q₁ to Q₃, whiskers = lowest and highest values):

| Plant | Box (Q₁ to Q₃) | IQR | Whiskers | Range |
|---|---|---|---|---|
| 1 | 95 to 103 | 8 | 85 to 109 | 24 |
| 2 | 82 to 100 | 18 | 65 to 118 | 53 |
| 3 | 99 to 106 | 7 | 88 to 117 | 29 |
| 4 | 78 to 85 | 7 | 73 to 94 | 21 |

#### Relationship between quality at the plants (centre)
- **Plant 3** has the highest quality index. Its box is the highest (99 to 106).
- **Plant 1** is next and is close to Plant 3. The two boxes overlap slightly.
- **Plant 2** has a lower, wider box (82 to 100). It overlaps Plants 1 and 4, so its typical quality lies between them.
- **Plant 4** has the lowest quality, with its whole box (78 to 85) below the boxes of Plants 1 and 3.

Order of average quality: Plant 3 ≥ Plant 1 > Plant 2 > Plant 4.

#### Variability
- **Plant 2** has by far the greatest variability. Its IQR (18) and range (53) are the largest, so its quality is the least predictable.
- **Plants 1, 3 and 4** have small and similar boxes (IQR 7 to 8), so they are consistent. Plant 4 has the smallest range (21) but a consistently low quality.
- **Plant 3** is both high in quality and consistent, so it is the best performer.

#### Conclusion
Plant 3 is the best (high and steady). Plant 1 is good and steady. Plant 4 is steady but low and needs improvement of the mean level. Plant 2 needs the most attention to reduce variation.

## Check yourself

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

1. Which plant has the greatest variability?
   A. Plant 1
   B. Plant 2, IQR 18 and range 53
   C. Plant 3
   D. Plant 4
   Answer: B. Widest box and whiskers. (Key point: Most variable)

2. Why is Plant 3 best?
   A. Lowest
   B. Largest range
   C. Highest box and small IQR
   D. Widest box
   Answer: C. High and consistent. (Key point: Best plant)

3. What is said of Plant 4?
   A. Highest quality
   B. Most variable
   C. Best
   D. Steady but lowest quality
   Answer: D. Box 78 to 85 is below others. (Key point: Lowest quality)

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