Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Aug 2610:00 AM EDT
-11:59 PM EDT
Save up to $1,000 on select GMAT prep now. This Fall, achieve your most ambitious goals with millions of student success stories behind you.
Aug 2710:00 AM EDT
-11:00 AM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Aug 3110:00 AM PDT
-11:00 AM EDT
Top Scores Start with a Elite Online Prep Course. Enroll for 6 months of access to over 400 hours of GMAT video lessons AND 715+ Score Guarantee!
Sep 0609:30 AM EDT
-12:30 PM EST
Top scores are possible when you enroll in a powerful EA course, taught live online + 6 months access to TTP OnDemand video courses included! Perfect class schedule and easy course access for working professionals. Class starts Sept. 6, 9:30am-12:30pm EST
Sep 0907:00 AM PDT
-10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway
07 Jul 2025, 08:00
Kudos
Bookmarks
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% (02:08) correct
38%
(02:14)
wrong
based on 411
sessions
History
Date
Time
Result
Not Attempted Yet
|
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
Kudos
Bookmarks
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
Bookmarks
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
