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25 Sep 2025, 03:36
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Removing BX-06 will decrease the standard deviation of weights in the remaining load.: False
Adding BX-Sub to the main load will reduce the standard deviation of weights.: True
The standard deviation of volumes will be most decreased if BX-10 is removed.: False
Eleven shipping crates were measured before loading. The table shows each crate’s weight (kg) and volume (m^3). The last row lists the average across the main load. The standard deviations of both weight and volume were also calculated for this main load.
For an actual trip, one or more crates may be excluded from the load, and one substitute crate (BX-Sub) may be added. BX-Sub was measured with a weight of 260 kg and a volume of 4.2 m^3.
For each of the following statements, select True if the statement is true based on the information provided. Otherwise, select False.
For an actual trip, one or more crates may be excluded from the load, and one substitute crate (BX-Sub) may be added. BX-Sub was measured with a weight of 260 kg and a volume of 4.2 m^3.
| Crate | Weight (kg) | Volume (m^3) |
|---|---|---|
| BX-01 | 160 | 4.4 |
| BX-02 | 180 | 3.8 |
| BX-03 | 200 | 5.1 |
| BX-04 | 220 | 4.0 |
| BX-05 | 240 | 3.9 |
| BX-06 | 260 | 4.2 |
| BX-07 | 280 | 3.6 |
| BX-08 | 300 | 4.6 |
| BX-09 | 320 | 4.1 |
| BX-10 | 340 | 3.5 |
| BX-11 | 360 | 4.8 |
| Average across main load | 260 | 4.18 |
For each of the following statements, select True if the statement is true based on the information provided. Otherwise, select False.
| True | False | |
| Removing BX-06 will decrease the standard deviation of weights in the remaining load. | ||
| Adding BX-Sub to the main load will reduce the standard deviation of weights. | ||
| The standard deviation of volumes will be most decreased if BX-10 is removed. |
ShowHide Answer
Official Answer
Removing BX-06 will decrease the standard deviation of weights in the remaining load.: False
Adding BX-Sub to the main load will reduce the standard deviation of weights.: True
The standard deviation of volumes will be most decreased if BX-10 is removed.: False
25 Sep 2025, 03:36
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Official Solution:
• Removing BX-06 will decrease the standard deviation of weights in the remaining load.
The standard deviation of a set shows how much the values deviate from the mean, that is, how widespread the set is. BX-06 is exactly at the mean weight (260), so it contributes zero deviation. Removing it leaves all nonzero deviations unchanged while reducing the count; here the mean of the remaining weights stays at 260, so those distances don’t shrink. With the same spread divided by fewer items, the average distance grows rather than falls. So, essentially, removing an item whose weight is equal to the mean weight makes the set more widespread, thus increasing the standard deviation.
Answer: False
• Adding BX-Sub to the main load will reduce the standard deviation of weights.
BX-Sub’s weight is 260, the current mean. Adding a value equal to the mean does not add any new deviation and does not shift the mean; it simply increases the count. The same total spread spread over more items makes the average distance from the mean smaller, so the standard deviation goes down.
Answer: True
• The standard deviation of volumes will be most decreased if BX-10 is removed.
The mean volume is about 4.18. BX-10, at 3.5, is 0.68 away from the mean. BX-03, however, at 5.1, is 0.92 away from the mean, which is farther than BX-10. Removing the single value with the largest absolute deviation reduces the standard deviation the most. Since BX-10 is not the farthest from the mean, removing it cannot produce the greatest decrease.
Answer: False
Correct answer:
Removing BX-06 will decrease the standard deviation of weights in the remaining load. "False"
Adding BX-Sub to the main load will reduce the standard deviation of weights. "True"
The standard deviation of volumes will be most decreased if BX-10 is removed. "False"
bb
• Removing BX-06 will decrease the standard deviation of weights in the remaining load.
The standard deviation of a set shows how much the values deviate from the mean, that is, how widespread the set is. BX-06 is exactly at the mean weight (260), so it contributes zero deviation. Removing it leaves all nonzero deviations unchanged while reducing the count; here the mean of the remaining weights stays at 260, so those distances don’t shrink. With the same spread divided by fewer items, the average distance grows rather than falls. So, essentially, removing an item whose weight is equal to the mean weight makes the set more widespread, thus increasing the standard deviation.
Answer: False
• Adding BX-Sub to the main load will reduce the standard deviation of weights.
BX-Sub’s weight is 260, the current mean. Adding a value equal to the mean does not add any new deviation and does not shift the mean; it simply increases the count. The same total spread spread over more items makes the average distance from the mean smaller, so the standard deviation goes down.
Answer: True
• The standard deviation of volumes will be most decreased if BX-10 is removed.
The mean volume is about 4.18. BX-10, at 3.5, is 0.68 away from the mean. BX-03, however, at 5.1, is 0.92 away from the mean, which is farther than BX-10. Removing the single value with the largest absolute deviation reduces the standard deviation the most. Since BX-10 is not the farthest from the mean, removing it cannot produce the greatest decrease.
Answer: False
Correct answer:
Removing BX-06 will decrease the standard deviation of weights in the remaining load. "False"
Adding BX-Sub to the main load will reduce the standard deviation of weights. "True"
The standard deviation of volumes will be most decreased if BX-10 is removed. "False"
04 Nov 2025, 22:01
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Bunuel
I've a doubt with regarding question-1.
Question-1 stem says "For an actual trip, one or more crates may be excluded from the load, [b]and one substitute crate (BX-Sub) may be added[/b]"... that means --- we are removing one or more crates and simultaneously adding BX-sub which is of same specification as BX-06.
Now question stem-1 doesnt says that - BX-06 is "only" is being removed,, further, whenever a box BX-06 is removed BX-sub replaces it.. under which condition Standard deviation should remains same as opposite to your explaination of STd deviation decreasing. though answer in both case remains "False".
I've a doubt with regarding question-1.
Question-1 stem says "For an actual trip, one or more crates may be excluded from the load, [b]and one substitute crate (BX-Sub) may be added[/b]"... that means --- we are removing one or more crates and simultaneously adding BX-sub which is of same specification as BX-06.
Now question stem-1 doesnt says that - BX-06 is "only" is being removed,, further, whenever a box BX-06 is removed BX-sub replaces it.. under which condition Standard deviation should remains same as opposite to your explaination of STd deviation decreasing. though answer in both case remains "False".
