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10 Dec 2020, 01:12
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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
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (02:57) correct
58%
(03:03)
wrong
based on 205
sessions
History
Date
Time
Result
Not Attempted Yet
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.
1.jpg [ 100.35 KiB | Viewed 4533 times ]
| 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.
Attachment:
1.jpg [ 100.35 KiB | Viewed 4533 times ]
| 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. |
ShowHide Answer
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
24 Nov 2024, 11:54
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Bunuel
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 - 0.92 ≈ 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"
12 Dec 2024, 12:38
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1. For each statement, we need to check whether it can be supported or not by information.
2. The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range. Let's calculate all of the ranges: Pipe Length. 18.50 - 8.70 = 9.8; Pipe Width. 15.00 - 2.32 = 12.68; Bowl height. 24.00 - 4.92 = 19.08; Bore diameter. 8.90 - 1.76 = 7.14; Bowl diameter. 4 - 0.98 = 3.02; Bowl Depth. 4.85 - 1.75 = 3.1. The medians for Bowl height and Bowl diameter are 10 and 2.47, which have a ratio more than 4. So, this statement can be supported.
3. The bowl height for each style of pipe is at least twice the bowl depth. The canine style has a ratio of \(\frac{4.92}{2.92} \approx 1.68 < 2\). So, this statement is not supported.
4. The standard deviation of pipe lengths is less than the standard deviation of bowl heights. The average of the two values is equal to 11.884 and 10.678, respectively. The standard deviation of pipe lengths = \(\sqrt{\frac{152}{10}} \approx 3.9\) and the standard deviation of bowl heights = \(\sqrt{\frac{281}{10}} \approx 5.3\). 3.9 < 5.3. So, this statement can be supported.
2. The median of a characteristic with the largest range is more than four times the median of a characteristic with the smallest range. Let's calculate all of the ranges: Pipe Length. 18.50 - 8.70 = 9.8; Pipe Width. 15.00 - 2.32 = 12.68; Bowl height. 24.00 - 4.92 = 19.08; Bore diameter. 8.90 - 1.76 = 7.14; Bowl diameter. 4 - 0.98 = 3.02; Bowl Depth. 4.85 - 1.75 = 3.1. The medians for Bowl height and Bowl diameter are 10 and 2.47, which have a ratio more than 4. So, this statement can be supported.
3. The bowl height for each style of pipe is at least twice the bowl depth. The canine style has a ratio of \(\frac{4.92}{2.92} \approx 1.68 < 2\). So, this statement is not supported.
4. The standard deviation of pipe lengths is less than the standard deviation of bowl heights. The average of the two values is equal to 11.884 and 10.678, respectively. The standard deviation of pipe lengths = \(\sqrt{\frac{152}{10}} \approx 3.9\) and the standard deviation of bowl heights = \(\sqrt{\frac{281}{10}} \approx 5.3\). 3.9 < 5.3. So, this statement can be supported.
