Question

Multiple Choice Question
The table lists the numbers of rolls of paper towels produced each day this week by two companies.

Paper Giant Wipe It Clean
653 756
647 582
651 734
658 542
655 784
Which inference can be drawn from the data?

A.
The workers at Wipe It Clean are more consistent than the workers at Paper Giant.

B.
Wipe It Clean shows a wider variation in the numbers of paper towels produced than Paper Giant.

C.
On average, Paper Giant produces more paper towels than Wipe It Clean.

D.
The data for Paper Giant has a higher median than the data for Wipe It Clean.

Answer 1

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:

1. **Mean (Average)**:
- Paper Giant:
\[
\text{Mean} = \frac{653 + 647 + 651 + 658 + 655}{5} = \frac{3164}{5} = 632.8
\]
- Wipe It Clean:
\[
\text{Mean} = \frac{756 + 582 + 734 + 542 + 784}{5} = \frac{3898}{5} = 779.6
\]

2. **Range (to assess consistency and variation)**:
- Paper Giant:
\[
\text{Range} = 658 - 647 = 11
\]
- Wipe It Clean:
\[
\text{Range} = 784 - 542 = 242
\]

3. **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

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.**