Subjects statistics

Box Plot Summary Ec8972

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We are given the data set representing the number of customers at Slurpee Sam's Spaghetti Shop: 24, 25, 29, 30, 31, 31, 32, 34, 34. 2. **Find the five-number summary:** This includes the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. - Minimum = 24 - Maximum = 34 3. **Find the median (Q2):** Since there are 9 data points (odd number), the median is the middle value when data is sorted. Sorted data: 24, 25, 29, 30, 31, 31, 32, 34, 34 Median (5th value) = 31 4. **Find Q1:** Median of the lower half (first 4 values: 24, 25, 29, 30) Q1 = average of 2nd and 3rd values = \frac{25 + 29}{2} = \frac{54}{2} = 27 5. **Find Q3:** Median of the upper half (last 4 values: 31, 32, 34, 34) Q3 = average of 2nd and 3rd values = \frac{32 + 34}{2} = \frac{66}{2} = 33 6. **Summary:** - Minimum = 24 - Q1 = 27 - Median = 31 - Q3 = 33 - Maximum = 34 7. **Compare with box plot options:** - Option A: whiskers 24 to 34, box 27 to 33, median 31 - Option B: whiskers 24 to 34, box 29 to 32, median 31 - Option C: whiskers 24 to 34, box 27 to 33, median 31 Option A and C have the correct box from 27 to 33 and median 31. 8. **Check the median in option C:** It says median near 32, but our median is 31. Therefore, **Option A** correctly summarizes the data. **Final answer:** Option A