- 2074 Asoj · 7 marks
Interpret box plots of four plants
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.
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.]
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.
✓ Answer checked by Claude Sonnet 5.5
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