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13 Jan 2026, 12:36
Kudos
Bookmarks
Most decrease: 56
Most increase: 38
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.
{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.
| Most decrease | Most increase | |
| 23 | ||
| 24 | ||
| 34 | ||
| 38 | ||
| 53 | ||
| 56 |
ShowHide Answer
Official Answer
Most decrease: 56
Most increase: 38
13 Jan 2026, 12:36
Kudos
Bookmarks
Official Solution:
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.
Correct answer:
Most decrease "56"
Most increase "38"
Bunuel
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.
Correct answer:
Most decrease "56"
Most increase "38"
