To find the five-number summary for 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 the minimum \( (0) \), first quartile \( (Q1)\) which is the median of the first half \((2)\), the median \((Q2)\) which is \(4\), third quartile \( (Q3)\) which is the median of the second half \((7)\), and the maximum \( (8) \). Thus, the five-number summary is \(0, 2, 4, 7, 8\).
To create a box plot, we can plot these five values: the box extends from \(Q1 (2)\) to \(Q3 (7)\) with a line at the median \( (4) \), and the 'whiskers' extend to the minimum \( (0)\) and maximum \( (8)\). The box plot shows that the data is slightly right-skewed, as the right whisker (maximum) is longer than the left whisker (minimum), indicating a concentration of values towards the lower end of the range. This suggests that while some days saw more eggs, there were also several days with very low counts, which may indicate variability in egg production.