Use the table to answer the question.

Pick up Browse Total
Weekday 25 12 37
Weekend 17 45 62
Total 42 57 99
Sal kept track of how many people visited the local library and recorded their purpose for visiting. Using marginal relative frequency, what interpretation can you make from the data in the two-way table?

(1 point)
Responses

A high percentage of people pick up on the weekend.
A high percentage of people pick up on the weekend.

The pick-up service is not very popular at this library.
The pick-up service is not very popular at this library.

The weekend is the most popular time to visit.
The weekend is the most popular time to visit.

People only come to pick up reserved books during the week.
People only come to pick up reserved books during the week.

1 answer

To determine the correct interpretation using marginal relative frequency, let's first calculate some relevant percentages using the totals from the table.

Total Visitors:

  • Total: 99
  • Weekday total: 37
  • Weekend total: 62

Marginal Relative Frequencies:

  1. Percentage of visitors who pick up on weekdays: \[ \frac{25}{99} \approx 0.2525 \text{ or } 25.25% \]

  2. Percentage of visitors who browse on weekdays: \[ \frac{12}{99} \approx 0.1212 \text{ or } 12.12% \]

  3. Percentage of visitors who pick up on weekends: \[ \frac{17}{99} \approx 0.1717 \text{ or } 17.17% \]

  4. Percentage of visitors who browse on weekends: \[ \frac{45}{99} \approx 0.4545 \text{ or } 45.45% \]

Analysis:

  • On weekdays, 25 visitors picked up (25.25%), while only 12 browsed (12.12%). Therefore, the pick-up service is more utilized on weekdays compared to weekends.

  • On weekends, the browsing activity is significantly higher with 45 visitors (45.45%) compared to only 17 who picked up (17.17%).

Based on the data and calculations, the most fitting interpretation from the given responses is:

A high percentage of people pick up on the weekend. (This is not accurate since more people choose to browse on weekends rather than picking up.)

Therefore, the better response would be: The pick-up service is not very popular at this library. Most visitors prefer to browse on weekends, indicating the pick-up service has limited appeal.

Hence, the correct choice according to the marginal relative frequency analysis is:

The pick-up service is not very popular at this library.