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14 Oct 2025, 06:37
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The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers: Not necessarily true
The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number: True
The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers: Not necessarily true
The table shows, for one recent month, visitor numbers for 8 city library branches. Each entry is a count of people rounded down to the nearest hundred.
For each statement below, select True if it can be verified to be true based on the table provided. Otherwise, select Not necessarily true.
| Branch | Average weekday visitors | Average weekend visitors | Record single-day visitors |
|---|---|---|---|
| Ash | 1300 | 1400 | 3800 |
| Birch | 1500 | 1500 | 3600 |
| Cedar | 1400 | 1400 | 3100 |
| Dogwood | 900 | 1200 | 2300 |
| Elm | 1600 | 1600 | 4200 |
| Fir | 1600 | 1600 | 4200 |
| Grove | 1200 | 1400 | 2700 |
| Holly | 1100 | 1300 | 2600 |
For each statement below, select True if it can be verified to be true based on the table provided. Otherwise, select Not necessarily true.
| True | Not necessarily true | |
| The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers | ||
| The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number | ||
| The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers |
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Official Answer
The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers: Not necessarily true
The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number: True
The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers: Not necessarily true
14 Oct 2025, 06:37
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Official Solution:
• The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers.
The median is the average of the fourth and fifth values after sorting. For average weekday visitors, these are 1,300 and 1,400. Since all figures are rounded down to the nearest hundred, the smallest possible median would be the average of 1,300 and 1,400, which is 1,350. The largest possible median would be the average of 1,399 and 1,499, which is 1,449. Therefore, the true weekday median lies between 1,350 and 1,449.
For average weekend visitors, the fourth and fifth values are both 1,400. Because each could represent a true value anywhere from 1,400 to 1,499, the true weekend median lies between 1,400 and 1,499.
Since these two ranges overlap, we cannot verify that the weekend median is smaller than the weekday median.
Answer: Not necessarily true
• The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number.
The highest record single-day visitor number is 4200 (Elm and Fir), and the lowest is shown as 2300 (Dogwood). Because the numbers are rounded down to the nearest hundred, the true highest could be as low as 4200, while the true lowest could be as high as 2399. To get the lowest possible difference, we take the smallest possible value of the highest (4200) and the largest possible value of the lowest (2399). Using these gives 4200/2399, which is slightly more than 1.75. This means the highest branch has at least 75% more visitors than the lowest.
Answer: True
• The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers.
The lowest weekday values are Dogwood, Holly, Grove, and Ash. The lowest weekend values are Dogwood, Holly, and two of the 1400 group (Ash, Cedar, or Grove). Because rounding down could shift which of the 1400 branches is actually lower, the sets may not match exactly.
Answer: Not necessarily true
Correct answer:
The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers "Not necessarily true"
The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number "True"
The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers "Not necessarily true"
Bunuel
• The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers.
The median is the average of the fourth and fifth values after sorting. For average weekday visitors, these are 1,300 and 1,400. Since all figures are rounded down to the nearest hundred, the smallest possible median would be the average of 1,300 and 1,400, which is 1,350. The largest possible median would be the average of 1,399 and 1,499, which is 1,449. Therefore, the true weekday median lies between 1,350 and 1,449.
For average weekend visitors, the fourth and fifth values are both 1,400. Because each could represent a true value anywhere from 1,400 to 1,499, the true weekend median lies between 1,400 and 1,499.
Since these two ranges overlap, we cannot verify that the weekend median is smaller than the weekday median.
Answer: Not necessarily true
• The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number.
The highest record single-day visitor number is 4200 (Elm and Fir), and the lowest is shown as 2300 (Dogwood). Because the numbers are rounded down to the nearest hundred, the true highest could be as low as 4200, while the true lowest could be as high as 2399. To get the lowest possible difference, we take the smallest possible value of the highest (4200) and the largest possible value of the lowest (2399). Using these gives 4200/2399, which is slightly more than 1.75. This means the highest branch has at least 75% more visitors than the lowest.
Answer: True
• The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers.
The lowest weekday values are Dogwood, Holly, Grove, and Ash. The lowest weekend values are Dogwood, Holly, and two of the 1400 group (Ash, Cedar, or Grove). Because rounding down could shift which of the 1400 branches is actually lower, the sets may not match exactly.
Answer: Not necessarily true
Correct answer:
The median of the average weekend visitor numbers is smaller than the median of the average weekday visitor numbers "Not necessarily true"
The branch with the highest record single-day visitor number has at least 75 percent more visitors than the branch with the lowest such number "True"
The four branches with the least average weekday visitor numbers are the same four branches with the least average weekend visitor numbers "Not necessarily true"
liberoasperiores
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14 Jan 2026, 10:14
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Hi Bunuel
I interpreted the second statement as the comparison between the two branches across the week. Could you help me understand, how here it is to be compared on the record single day visitor column values.?
I interpreted the second statement as the comparison between the two branches across the week. Could you help me understand, how here it is to be compared on the record single day visitor column values.?
Bunuel
