To find the five-number summary of the dataset \(5, 8, 0, 3, 2, 7, 4\), we first organize the data in ascending order: \(0, 2, 3, 4, 5, 7, 8\). The five-number summary consists of:
- Minimum: \(0\)
- First Quartile (Q1): \(2\)
- Median (Q2): \(4\)
- Third Quartile (Q3): \(7\)
- Maximum: \(8\)
The box plot would have a box extending from Q1 (2) to Q3 (7), with a line at the median (4) inside the box. The "whiskers" would extend from the minimum (0) to Q1 (2) and from Q3 (7) to the maximum (8).
The box plot indicates that the data is slightly skewed to the left, as the median is closer to the upper quartile than the lower quartile. This suggests that while most days have a reasonable number of eggs laid, there are some days (like the day when only 0 eggs were laid) that significantly lower the overall average, affecting the distribution. Overall, the distribution shows variability in the number of eggs laid with a notable minimum day but otherwise relatively consistent egg production.