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805+ Level|   Math Related|         
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 09:58
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m = -0.5n + 10
Mean original = 7.3
SD original = 2.9

Mean is affected by multiplication(scale) and addition(shifts) of individual terms
Corrected mean = -0.5(7.3) + 10 = 6.35

SD is affected by multiplication(scale) only of individual terms. Also, SD is always positive
Corrected SD = 0.5(2.9) = 1.45
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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.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:01
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Given:
Correct result > -0.5n + 10
OG mean - 7.3
OG std deviation - 2.9

Corrected mean = -0.5* 7.3 + 10 = 6.35

Corrected std deviation = 2.9*0.5 = 1.45 (only 0.5 - the scaling factor impacts standard deviation)
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:02
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The corrected result is calculated by multiplying the original value by -0.5 and then adding 10. To find the corrected mean, you apply this formula to the average of the original measurements: multiply 7.3 by -0.5 and add 10, which gives 6.35. For the corrected standard deviation, since adding a constant doesn’t change variability, you only multiply the original standard deviation by the absolute value of -0.5. So, 2.9 times 0.5 equals 1.45. Therefore, the corrected mean is 6.35 and the corrected standard deviation is 1.45.
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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.
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Using the property of addition and multiplication for Average and Standard deviation that is

Average is shifter when the data points are multiplied by a certain number Therefore the average after multiplication with -0.5 = 7.3* (-0.5) = -3.65
and is also after by the addition of ceratin value to all datapoint by same factor . Hence new Average = -3.65 + 10 = 6.35 Answer.

Standard deviation is only affected by multiplication and not by addition. So the new Standard deviation is 2.9 * (-0.5) = -1.45 Answer.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:23
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We are given that:

\(m = -0.5n + 10\)

Here, m = corrected value
n = observed value

Before we proceed, we need to understand the effect of addition and multiplication on both mean and SD.

For mean: If there is a set {a,b,c} with mean x; and we add 10 to each of the values in the set, then the set becomes {a+10,b+10,c+10} and the corresponding new mean becomes x+10
This same principle is applicable for "mean" when we multiply the set values with another value

For SD: First thing to note is that SD can never be negative, since this tells us the spread of the data
Secondly, addition and subtraction to the set values has no effect on SD. Only multiplication and division change the SD.
For e.g., if we have a set {a,b,c} with SD = S; and we multiply all the values in the set with 10, then the set becomes {10a, 10b, 10c} and the new SD = 10S


Using the above, we can say that for the corrected mean:

we have, \(7.3(-0.5)+10 = 6.35\)

For the corrected SD, we have:

\(2.9(0.5) = 1.45\)


Answer:

Corrected mean: 6.35
Corrected SD: 1.45
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:36
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mean is affected by both multiplication and addition.
hence corrected mean = -0.5*7.3+10 = 6.35

SD is affected only by multiplication and not by addition
hence corrected SD= -0.5*2.9 = -1.45

Answers are:
Corrected Mean = 6.35
Corrected Standard Deviation = -1.45
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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.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:41
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The average will be affected by the coefficient (impact magnitude) and the subsequent addition or subtraction.
So for m = -0.5n + 10, the average (M) = -0.5 (original average) + 10.
Thus, we get the answer:
-0.5 7.3 + 10 = -3.65 + 10 = 6.35


The standard deviation is only affected by the absolute value of the coefficient, and the subsequent addition or subtraction does not affect the standard deviation.
Therefore,
|-0.5| 2.9 = 1.45
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:43
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let each value be 7.3

new value is -0.5(7.3) + 10 --> -3.65 + 10 --> 6.35

standard deviation: +10 wont have any impact on std.dev
but as all the values are halved the std.deviation also gets halved to 1.45
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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.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 10:44
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Whenever all the values in set are added and subtracted by same number, lets say "a" :

New Mean (new) = Mean (old) + a(with sign)*
Standard Deviation (new) = SD (old)

Whenever all the values in set are multiplied and divided by a number (lets say "a":
New Mean = Mean * a
SD (new) = SD (old) * |a|

So, Mean (Original) = 7.3 and SD (original) = 2.9

Mean (new)= -0.5 (7.3) + 10 = 6.35
SD (new) -0.5*2.9= -1.45

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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.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 11:27
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New Shifted number m = -0.5n + 10

Each number multiplied by -0.5 and 10 additional

Then Sum = -0.5n1+10+..........(-0.5n7+10)
=-0.5(n1+n2+.....+n7)+70

Mean. = -0.5*7.3+10 = 6.35

SD will only change by a multiplied number, but always positiv,e then SD = 0.5*2.9 = 1.45
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 11:29
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A calibration error on a science experiment.

Correct results are M= -0.5n+10 where n was the original
m= corrected value
n = original


mean (average) of original values is = 7.3
standard deviation is 2.9

Find the corrected mean and corrected standard deviation.

Corrected mean = -0.5 * 7.3 + 10 = 6.35
Corrected SD = -0.5 x2.9 = |1.45| (+ because SD is +)


C Mean = 6.35
C SD = 1.45
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Properties to remember:

w.r.t to mean
1. When a number is added or subtracted-SD dont chage
2. When a number is * or divided: SD is changed to the same fraction

w.r.t to SD
1. When a number is added or subtracted: Mean will increase or decrease by the same number
2. When a number is multiplied or divided, Mean will change by the same fraction




With this we will be able to find 6.35 and -1.45 as revised mean and SD
Mean =-1/2*7.3+10=6.35
SD=(29/10)*-1/2=-1.45
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 11:39
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New mean will be -0.5*older mean + 10 = -0.5*7.9 + 10 = 6.35

New standard deviation will be |-0.5|*2.9 = 1.45

Answer is (6.35, 1.45)
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corrected mean = -0.5*(mean) + 10 = -0.5*(7.3) + 10 = 6.35
corrected SD = -0.5*(SD) = -0.5*2.9 = -1.45
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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.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 12:11
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Bunuel
 


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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.
Show more

Multiplication and addition both affect Mean, hence -

Corrected Mean = -(0.5 * 7.3) + 10 = -3.65 + 10 = 6.35

Only multiplication of a constant affects SD, hence -

Corrected SD = |-0.5| * 2.9 = 1.45

Answers

Corrected Mean = 6.35
Corrected SD = 1.45
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 12:21
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Bunuel
 


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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.
Show more

The corrected result m = -0.5*n + 10 , where n was the original recorded value.

The average (A.M) of the original measurement = 7.3.

Suppose if there is a single value. Then n = 7.3

Then the corrected mean m = -0.5*(7.3)+10 = -3.65+10 = 6.35

Option C

S.D for the corrected result:

The term m = -0.5n +10

Contains a multiplication term and an addition term. The addition to a set a value doesn’t affect the S.D. Thus, increasing or decreasing the value by a common term doesn’t change the standard deviation.

Hence, +10 contains no effect.

m = -0.5*n

Multiplying or dividing the S.D of the element by x, the new S.D becomes |x| * old S.D (or) new S.D = old S.D /(x)

Corrected S.D = |-0.5| * 2.9 = 1.45

Option D
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 12:27
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We are given: m = -0.5n + 10
As per properties:
Corrected mean: =a* original mean+b
Corrected standard deviation: =|a|* original std
Here, a=−0.5, b= 10 and original mean and std is 7.3 and 2.9 respectively.

putting values:

Corrected mean
= (-0.5)(7.3)*10
= 6.35

Corrected standard deviation
= (0.5)*2.9
= 1.45
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 12:33
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The standard deviation measures data spread. Adding a constant (like +10) just shifts data, not its spread. Multiplying by a constant (like -0.5) scales the spread, so you multiply the original standard deviation (2.9) by the absolute value of that constant (0.5), resulting in 1.45.

Regards,
Lucas
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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.
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GMAT Club Olympics 2025 (Day 6): During a science experiment 07 Jul 2025, 13:15
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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.
Show more

Effect on Average = Multiply by -0.5 and then add 10

New Mean = -0.5 * 7.3 = -3.65

-3.65 + 10 = 6.35

Effect on Standard Deviation = 0.5 * 2.9 = 1.45

Final Answers

Corrected Mean = 6.35
Corrected Standard Deviation = 1.45
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Solution:

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.

To calculate the Corrected Mean, the formula is m = -0.5(7.3) + 10 = 6.35.

To calculate the Corrected SD, the formula is m= -0.5(2.9) + 10 = 8.55.



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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.
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