To find the five-number summary from the dataset (5, 8, 0, 3, 2, 7, 4), we will first sort the data:
Sorted data: 0, 2, 3, 4, 5, 7, 8
Five-Number Summary
- Minimum: 0
- First Quartile (Q1): The median of the first half (0, 2, 3) = 2
- Median (Q2): The median of the dataset (4)
- Third Quartile (Q3): The median of the second half (5, 7, 8) = 7
- Maximum: 8
Thus, the five-number summary is:
- Minimum: 0
- Q1: 2
- Median: 4
- Q3: 7
- Maximum: 8
Box Plot
To create a box plot based on the five-number summary, we can represent the values on a number line:
0 2 4 7 8
|---|-----|--------|------|
[----------]
- The box spans from Q1 (2) to Q3 (7).
- The line inside the box represents the median (4).
- Whiskers extend from the minimum (0) to Q1 (2) and from Q3 (7) to the maximum (8).
Description of the Distribution
From the box plot, we can see that the distribution of eggs laid has a slight right skew. The median (4) is towards the lower end of the box, indicating that while most of the data points are concentrated around the lower values (0 to 4), there are a few higher values (5 to 8) that pull the mean upward. The long whisker on the right side, extending to the maximum (8), indicates that some days have significantly higher egg counts, which suggests variability in the daily egg production.
Explanation of Distribution
The distribution indicates that while the average number of eggs laid is moderate, there's a mix of low counts (including days with no eggs) and some higher counts, which could suggest factors affecting egg production such as chicken health, feeding, or environmental conditions. The presence of a zero in the data may represent days when hens are not laying, and the range reflects variability in egg-laying patterns throughout the week.