To determine which inference can be drawn from the data, we will analyze the daily production numbers of both companies:
Paper Giant:
653, 647, 651, 658, 655
Wipe It Clean:
756, 582, 734, 542, 784
Let's calculate some key statistics for both companies:
-
Mean (Average):
- Paper Giant: \[ \text{Mean} = \frac{653 + 647 + 651 + 658 + 655}{5} = \frac{3164}{5} = 632.8 \]
- Wipe It Clean: \[ \text{Mean} = \frac{756 + 582 + 734 + 542 + 784}{5} = \frac{3898}{5} = 779.6 \]
-
Range (to assess consistency and variation):
- Paper Giant: \[ \text{Range} = 658 - 647 = 11 \]
- Wipe It Clean: \[ \text{Range} = 784 - 542 = 242 \]
-
Median (to analyze the central tendency):
- Paper Giant (sorted): 647, 651, 653, 655, 658
Median = 653 - Wipe It Clean (sorted): 542, 582, 734, 756, 784
Median = 734
- Paper Giant (sorted): 647, 651, 653, 655, 658
Now, let's analyze the statements:
A. The workers at Wipe It Clean are more consistent than the workers at Paper Giant.
- This is false; Wipe It Clean has a wider range and is less consistent.
B. Wipe It Clean shows a wider variation in the numbers of paper towels produced than Paper Giant.
- This is true; the range of Wipe It Clean (242) is much wider than that of Paper Giant (11).
C. On average, Paper Giant produces more paper towels than Wipe It Clean.
- This is false; Paper Giant's average production (632.8) is less than Wipe It Clean's average (779.6).
D. The data for Paper Giant has a higher median than the data for Wipe It Clean.
- This is false; Paper Giant's median (653) is less than Wipe It Clean's median (734).
Based on this analysis, the correct inference is:
B. Wipe It Clean shows a wider variation in the numbers of paper towels produced than Paper Giant.
1 answer