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24 Dec 2025, 09:00
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Most decrease: 56
Most increase: 38
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:
56% (02:18) correct
44%
(02:43)
wrong
based on 221
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A quality inspector recorded the fill volumes, in milliliters, of six bottles from a production run, with the following results:
{24, 38, 53, 23, 56, 34}
The inspector believes exactly one of the six measurements is erroneous and will discard that measurement. To evaluate the impact of the discard, he will calculate the standard deviation of the original six measurements and the standard deviation of the remaining five measurements.
Select for Most decrease the measurement which, if discarded, would produce the greatest decrease in standard deviation, and select for Most increase the measurement which, if discarded, would produce the greatest increase in standard deviation. Make only two selections, one in each column.
I31-34
| Most decrease | Most increase | |
| 23 | ||
| 24 | ||
| 34 | ||
| 38 | ||
| 53 | ||
| 56 |
ShowHide Answer
Official Answer
Most decrease: 56
Most increase: 38
24 Dec 2025, 10:00
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A quality inspector recorded the fill volumes, in milliliters, of six bottles from a production run, with the following results:
{24, 38, 53, 23, 56, 34}
The inspector believes exactly one of the six measurements is erroneous and will discard that measurement. To evaluate the impact of the discard, he will calculate the standard deviation of the original six measurements and the standard deviation of the remaining five measurements.
Select for Most decrease the measurement which, if discarded, would produce the greatest decrease in standard deviation, and select for Most increase the measurement which, if discarded, would produce the greatest increase in standard deviation. Make only two selections, one in each column.
First find the mean of the original six measurements.
Mean = (23 + 24 + 34 + 38 + 53 + 56)/6 = 38.
Standard deviation depends on how far the numbers are from the mean (and larger distances matter much more).
Most decrease:
Removing the single value with the largest absolute distance from the mean reduces the standard deviation the most. 56 is farthest from the mean 38 (it is 18 away). Since it has the largest distance from the mean, discarding 56 reduces the spread the most. So Most decrease is 56.
Most increase:
38 is exactly the mean, so it contributes the least deviation among the six numbers: zero. Hence, discarding 38 removes none of the “spread” but leaves only five numbers with the same mean of 38, so the average spread among the remaining values becomes larger. This produces the greatest increase in standard deviation. Thus, removing an item whose value is equal to the mean value makes the set more widespread, increasing the standard deviation. So Most increase is 38.
GMAT-Club-Forum-ywx7rw4v.png [ 14.32 KiB | Viewed 1412 times ]
{24, 38, 53, 23, 56, 34}
The inspector believes exactly one of the six measurements is erroneous and will discard that measurement. To evaluate the impact of the discard, he will calculate the standard deviation of the original six measurements and the standard deviation of the remaining five measurements.
Select for Most decrease the measurement which, if discarded, would produce the greatest decrease in standard deviation, and select for Most increase the measurement which, if discarded, would produce the greatest increase in standard deviation. Make only two selections, one in each column.
GMAT Club Official Explanation:
First find the mean of the original six measurements.
Mean = (23 + 24 + 34 + 38 + 53 + 56)/6 = 38.
Standard deviation depends on how far the numbers are from the mean (and larger distances matter much more).
Most decrease:
Removing the single value with the largest absolute distance from the mean reduces the standard deviation the most. 56 is farthest from the mean 38 (it is 18 away). Since it has the largest distance from the mean, discarding 56 reduces the spread the most. So Most decrease is 56.
Most increase:
38 is exactly the mean, so it contributes the least deviation among the six numbers: zero. Hence, discarding 38 removes none of the “spread” but leaves only five numbers with the same mean of 38, so the average spread among the remaining values becomes larger. This produces the greatest increase in standard deviation. Thus, removing an item whose value is equal to the mean value makes the set more widespread, increasing the standard deviation. So Most increase is 38.
Attachment:
GMAT-Club-Forum-ywx7rw4v.png [ 14.32 KiB | Viewed 1412 times ]
General Discussion
24 Dec 2025, 09:54
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Mean = (24+38+53+23+56+34)/6 = 38
Max decrease in SD happens when a value farthest away from mean is removed, which is 56
Max increase in SD happens when a value closest to mean is removed, which is 38, the mean itself
| Values | 23 | 24 | 34 | 38 | 53 | 56 | |
| Difference from Mean | -15 | -14 | -4 | 0 | 15 | 28 | |
Max decrease in SD happens when a value farthest away from mean is removed, which is 56
Max increase in SD happens when a value closest to mean is removed, which is 38, the mean itself
Bunuel
