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07 Jul 2025, 08:00
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Corrected Mean: 6.35
Corrected Standard Deviation: 1.45
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:
62% (02:07) correct
38%
(02:16)
wrong
based on 371
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During a science experiment, each measurement result was affected by the same calibration error and had to be adjusted. The corrected result m for each result was calculated as m = -0.5n + 10, where n was the original recorded value. The average (arithmetic mean) of the original measurements was 7.3 and the standard deviation of the original measurements was 2.9.
Select for Corrected Mean the average (arithmetic mean) of the corrected results, and select for Corrected Standard Deviation the standard deviation of the corrected results. Make only two selections, one in each column.
| Corrected Mean | Corrected Standard Deviation | |
| 17.3 | ||
| 8.55 | ||
| 6.35 | ||
| 1.45 | ||
| -1.45 | ||
| -3.65 |
ShowHide Answer
Official Answer
Corrected Mean: 6.35
Corrected Standard Deviation: 1.45
07 Jul 2025, 08:30
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Bunuel
GMAT Club Official Explanation:
Since each original measurement n was transformed into a corrected result m = -0.5n + 10, the corrected mean is simply the average of all the m values. But since this transformation is applied identically to each individual value, we can apply the same transformation directly to the original mean.
That is, the corrected mean is:
Corrected mean = -0.5 * (original mean) + 10
Corrected mean = -0.5 * 7.3 + 10 = -3.65 + 10 = 6.35
As for the standard deviation, two key properties are useful:
- If we multiply (or divide) all the numbers in a set by a non-zero constant, the standard deviation will be respectively multiplied or divided by the absolute value of that constant. For example, if the SD of \(\{a, \ b, \ c\}\) is \(s\), then the SD of \(\{2a, \ 2b, \ 2c\}\) will be \(2s\) and the SD of \(\{-3a, \ -3b, \ -3c\}\) will be \(s*|-3|=3s\).
- If we add (or subtract) a constant to all the numbers in a set, the standard deviation will NOT change. For example, if the SD of \(\{a, \ b, \ c\}\) is \(s\), then the SD of \(\{a+4, \ b+4, \ c+4\}\) or of \(\{a-1, \ b-1, \ c-1\}\) will also be \(s\).
Since the transformation is m = -0.5n + 10, the scaling factor is -0.5 and the shift is +10. The +10 has no effect on the standard deviation, and the multiplication by -0.5 scales the SD by |-0.5| = 0.5.
Original SD = 2.9
Corrected SD = |-0.5| * 2.9 = 1.45
General Discussion
07 Jul 2025, 08:31
Kudos
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Hi,
Mean is affected by both operations (+ or -) and (* or /) and since each term had to go through the correction same will be applied to mean leading to 6.35 as updated mean.
SD is only affected (* or /) operation so applying that part of correction to the given SD lead to 1.45. Remember SD can never be negative. It is a positive quantity and sign of the numbers in the set does not affect the SD.
For Ex: Original Set: 2, 4, 6, 8, 10
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
SD = √(40 / 5) = √8 = ~2.828
Case 1: Add 5 to each number: 7, 9, 11, 13, 15
Mean = 6 + 5 = 11
SD = unchanged : ~2.828
Case 2: Subtract 3 from each number: −1, 1, 3, 5, 7
Mean = 6 – 3 = 3
SD = still : ~2.828
Case 3: Multiply all numbers by 2 : 1, 2, 3, 4, 5
Mean = 6 × 2 = 12
SD = 2 × original SD = 2 × 2.828 = ~5.656
Case 4: Divide all numbers by 2 : 1, 2, 3, 4, 5
Mean = 6 / 2 = 3
SD = original SD / 2 = 2.828 / 2 = ~1.414
Cheers,
Keshav Sharma
Mean is affected by both operations (+ or -) and (* or /) and since each term had to go through the correction same will be applied to mean leading to 6.35 as updated mean.
SD is only affected (* or /) operation so applying that part of correction to the given SD lead to 1.45. Remember SD can never be negative. It is a positive quantity and sign of the numbers in the set does not affect the SD.
For Ex: Original Set: 2, 4, 6, 8, 10
Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
SD = √(40 / 5) = √8 = ~2.828
Case 1: Add 5 to each number: 7, 9, 11, 13, 15
Mean = 6 + 5 = 11
SD = unchanged : ~2.828
Case 2: Subtract 3 from each number: −1, 1, 3, 5, 7
Mean = 6 – 3 = 3
SD = still : ~2.828
Case 3: Multiply all numbers by 2 : 1, 2, 3, 4, 5
Mean = 6 × 2 = 12
SD = 2 × original SD = 2 × 2.828 = ~5.656
Case 4: Divide all numbers by 2 : 1, 2, 3, 4, 5
Mean = 6 / 2 = 3
SD = original SD / 2 = 2.828 / 2 = ~1.414
Cheers,
Keshav Sharma
