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12 Nov 2024, 03:05
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The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range.: Supported
The bowl height for each style of pipe is at least twice the bowl depth.: Not supported
The standard deviation of pipe lengths is less than the standard deviation of bowl heights.: Supported
The table presents the characteristics of certain artifact effigy pipes, smoking pipes designed to resemble figures or animals, with right cylindrical bowls. All measurements are in centimeters.
For each of the following statements, select Supported if the information in the table accurately supports the statement. Otherwise, select Not supported.
| Style | Pipe Length | Pipe Width | Bowl height | Bore diameter | Bowl diameter | Bowl Depth |
|---|---|---|---|---|---|---|
| Canine | 17.70 | 2.32 | 4.92 | 1.76 | 0.98 | 2.92 |
| Crouching man | 8.70 | 5.05 | 8.87 | 2.50 | 2.47 | 1.75 |
| Pipe holder | 10.72 | 6.66 | 13.49 | 2.75 | 2.37 | 3.10 |
| Pipe holder | 10.20 | 8.24 | 14.10 | 2.99 | 2.35 | 2.95 |
| Two-headed figure | 9.42 | 8.27 | 10.00 | 3.30 | 3.00 | 3.80 |
| Feline | 14.70 | 5.82 | 7.00 | 3.30 | 2.47 | 3.40 |
| Feline | 10.40 | 7.80 | 8.40 | 8.90 | 3.05 | 4.20 |
| Human-bird | 18.50 | 15.00 | 16.00 | 4.20 | 3.30 | 3.60 |
| Crouching woman | 18.50 | 14.00 | 24.00 | 4.45 | 4.00 | 4.85 |
For each of the following statements, select Supported if the information in the table accurately supports the statement. Otherwise, select Not supported.
| Supported | Not supported | |
| The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range. | ||
| The bowl height for each style of pipe is at least twice the bowl depth. | ||
| The standard deviation of pipe lengths is less than the standard deviation of bowl heights. |
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Official Answer
The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range.: Supported
The bowl height for each style of pipe is at least twice the bowl depth.: Not supported
The standard deviation of pipe lengths is less than the standard deviation of bowl heights.: Supported
12 Nov 2024, 03:05
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Official Solution:
Statement 1:
Sorting by each characteristic, we find that the characteristic with the largest range is bowl height, with a range calculated as the largest value minus the smallest value: 24 - 4.92 ≈ 19 centimeters. The characteristic with the smallest range is bowl diameter, with a range of 4 - 0.98 ≈ 3 centimeters. The median, or middle value, of bowl heights is 10 centimeters, while the median of bowl diameters is 2.47 centimeters. Thus, the median of bowl heights is more than four times the median of bowl diameters. Therefore, this statement is Supported.
Statement 2:
Sorting the data by bowl height, we find that for a bowl height of 4.92 centimeters, the corresponding bowl depth is 2.92 centimeters, which is less than twice the depth. Therefore, this statement is Not supported.
Statement 3:
The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
Considering this, we observe that the data for pipe lengths, with an average of approximately 13 and ranging from 9 to 19, are less widespread than the data for bowl heights, with an average of approximately 12 and ranging from 5 to 24 (as you can see, the only thing we need to calculate to answer this question is the approximate average). Therefore, this statement is Supported.
Correct answer:
The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range. "Supported"
The bowl height for each style of pipe is at least twice the bowl depth. "Not supported"
The standard deviation of pipe lengths is less than the standard deviation of bowl heights. "Supported"
Bunuel
Statement 1:
Sorting by each characteristic, we find that the characteristic with the largest range is bowl height, with a range calculated as the largest value minus the smallest value: 24 - 4.92 ≈ 19 centimeters. The characteristic with the smallest range is bowl diameter, with a range of 4 - 0.98 ≈ 3 centimeters. The median, or middle value, of bowl heights is 10 centimeters, while the median of bowl diameters is 2.47 centimeters. Thus, the median of bowl heights is more than four times the median of bowl diameters. Therefore, this statement is Supported.
Statement 2:
Sorting the data by bowl height, we find that for a bowl height of 4.92 centimeters, the corresponding bowl depth is 2.92 centimeters, which is less than twice the depth. Therefore, this statement is Not supported.
Statement 3:
The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
Considering this, we observe that the data for pipe lengths, with an average of approximately 13 and ranging from 9 to 19, are less widespread than the data for bowl heights, with an average of approximately 12 and ranging from 5 to 24 (as you can see, the only thing we need to calculate to answer this question is the approximate average). Therefore, this statement is Supported.
Correct answer:
The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range. "Supported"
The bowl height for each style of pipe is at least twice the bowl depth. "Not supported"
The standard deviation of pipe lengths is less than the standard deviation of bowl heights. "Supported"
24 Nov 2024, 11:51
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I have revised the question, solution, and formatting by adding more details to enhance clarity.
