Question

1. a company tracked the daily number of customer complaints over two weeks: week 1: 3, 5, 7, 4, 6 week 2: 1, 2, 8, 9, 10 what is the best interpretation of the data? a. week 1 had a higher mean number of complaints than week 2. b. week 1 and week 2 had the same mean and variability. c. week 2 had less variability in complaints compared to week 1. d. week 2 had higher variability in complaints, while week 1 had a more consistent pattern.

Explanation:

1. First, calculate the mean for Week 1: The data is 3, 5, 7, 4, 6. The sum is \(3 + 5 + 7 + 4 + 6 = 25\), and the mean is \(\frac{25}{5}=5\). For Week 2: Data is 1, 2, 8, 9, 10. The sum is \(1 + 2 + 8 + 9 + 10 = 30\), and the mean is \(\frac{30}{5}=6\). So option a is incorrect.
2. Next, analyze variability (e.g., range). For Week 1, range is \(7 - 3 = 4\) (max - min). For Week 2, range is \(10 - 1 = 9\). A larger range means higher variability. So Week 2 has higher variability, and Week 1 has a more consistent pattern (smaller range). Option b is incorrect (means are different, variabilities too). Option c is incorrect (Week 2 has more variability). Option d matches the analysis.

Answer:

d. Week 2 had higher variability in complaints, while Week 1 had a more consistent pattern.