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Mileage of five different vehicles as reported by Jack were 16, 18, 11
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07 Jul 2025, 12:49
07 Jul 2025, 12:49
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Mileage of five different vehicles as reported by Jack were 16, 18, 11, 13 and 19 units. Two of the mileages were wrongly reported by jack, so that one was 5 units more than the correct value, and other was 5 units less than the correct value.
Quantity A |
Quantity B |
S.D. of reported mileages |
S.D. of actual mileages |
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Re: Mileage of five different vehicles as reported by Jack were 16, 18, 11
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11 Jul 2025, 01:09
11 Jul 2025, 01:09
Expert Reply
1. Mean is Unchanged: When one value in a dataset is increased by a certain amount (e.g., +5 ) and another value is decreased by the same amount (e.g., -5 ), the sum of the values remains unchanged. Since the number of values also remains the same, the mean of the dataset does not change.
2. Standard Deviation Depends on Specific Values: Standard deviation measures the spread of data points around the mean. Even if the mean is constant, changing individual data points can alter the spread.
- If the two changed values were initially far from the mean and are moved closer, the standard deviation would decrease.
- If the two changed values were initially close to the mean and are moved further away, the standard deviation would increase.
- If the changes happen to balance out in terms of squared deviations, the standard deviation could remain the same.
Since we don't know which specific two mileages (from 16, 18, 11, 13, 19) were wrongly reported, we cannot determine how their positions relative to the mean (15.4) changed, and thus we cannot determine whether the standard deviation of the actual mileages is greater than, less than, or equal to the standard deviation of the reported mileages.
2. Standard Deviation Depends on Specific Values: Standard deviation measures the spread of data points around the mean. Even if the mean is constant, changing individual data points can alter the spread.
- If the two changed values were initially far from the mean and are moved closer, the standard deviation would decrease.
- If the two changed values were initially close to the mean and are moved further away, the standard deviation would increase.
- If the changes happen to balance out in terms of squared deviations, the standard deviation could remain the same.
Since we don't know which specific two mileages (from 16, 18, 11, 13, 19) were wrongly reported, we cannot determine how their positions relative to the mean (15.4) changed, and thus we cannot determine whether the standard deviation of the actual mileages is greater than, less than, or equal to the standard deviation of the reported mileages.
gmatclubot
Re: Mileage of five different vehicles as reported by Jack were 16, 18, 11 [#permalink]
11 Jul 2025, 01:09
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