Q3 The following dataset represents the number of eggs laid in the chicken coop each day for the past week.

Question

5, 8, 0, 3, 2, 7, 4
In 3–5 sentences, find the five-number summary, create a box plot, and describe the distribution of data using the box plot and explain what the distribution means.

Minimum:
Quartile 1:
Median:
Quartile 3:
Maximum:

Answer 1

To find the five-number summary for the dataset \(5, 8, 0, 3, 2, 7, 4\), we start by sorting the data:

Sorted data: \(0, 2, 3, 4, 5, 7, 8\)

1. Minimum: \(0\) (the smallest value)
2. Quartile 1 (Q1): The median of the first half of the data (0, 2, 3) is \(2\).
3. Median: The median of the entire dataset (the middle value) is \(4\).
4. Quartile 3 (Q3): The median of the second half of the data (5, 7, 8) is \(7\).
5. Maximum: \(8\) (the largest value)

Thus, the five-number summary is:

• Minimum: \(0\)
• Q1: \(2\)
• Median: \(4\)
• Q3: \(7\)
• Maximum: \(8\)

Box Plot Description

To create a box plot:

• Draw a box from Q1 (\(2\)) to Q3 (\(7\)).
• A line inside the box indicates the median (\(4\)).
• "Whiskers" extend from the box to the minimum (\(0\)) and maximum (\(8\)).

Distribution Description

The distribution of the data shows a range from 0 to 8 eggs, with a median at 4. The lower quartile (2) suggests that a quarter of the days had 2 or fewer eggs laid, while the upper quartile (7) indicates that about 75% of the days had 7 or fewer eggs. The box plot indicates a somewhat asymmetrical distribution, with the upper half of the data (from the median to Quartile 3) being more spread out than the lower half. This may suggest that on some days, egg production was significantly higher, creating variability in daily egg counts. Overall, the data appears to have a central tendency around 4, with some days contributing to higher counts.