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The weights of a set of moving boxes on a truck have a mean of 22 poun 26 Oct 2021, 03:00
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The weights of a set of moving boxes on a truck have a mean of 22 pounds and a standard deviation of 3 pounds. Another 2 boxes are loaded onto the truck, one with a weight of 26 pounds and the other with a weight of 18 pounds. What effect does this have on the standard deviation of the weights of the boxes on the truck?

(A) The standard deviation does not change

(B) The standard deviation increases

(C) The standard deviation decreases

(D) It is not possible to determine whether the standard deviation decreases or stays the same, but it does not increase.

(E) It is not possible to determine whether the standard deviation increases or stays the same, but it does not decrease.
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The weights of a set of moving boxes on a truck have a mean of 22 poun 02 Jul 2023, 12:04
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AnujL
gmatophobia
Can you please explain this problem ?

plus, let say SD in this problem is 4 then the new SD of the boxes still increase or remain the same ?
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AnujL Standard deviation denotes how dispersed the data set is with respect to the mean.

In this question, we know that the mean weight of all the boxes is 22 pounds. The heavier box is 26 pounds (4 pounds above the mean) and the lighter box is 18 pounds (4 pounds below the mean). Hence after the two boxes that were added, the mean does not change and the mean of all the boxes is still 22 pounds.

Consider this - You've $22 with you, one friend gives you $4 and you lend $4 to another friend of yours. After both transactions, you will still have $22 with you.

Now back to the question - So after the two boxes are added the mean is still 22 pounds, however, we have added two data points which lie at some distance away from the mean. Hence the data set is now more dispersed and the SD increases.

Note:
1) The original value of standard deviation is not of any relevance to this question. So whether you take the original SD as 3, 4, or 2, the analysis and the behavior that the standard deviation increases remain the same.
2) We were able to arrive at the conclusion only because the value of the mean didn't change.
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The weights of a set of moving boxes on a truck have a mean of 22 poun 27 Oct 2021, 01:41
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Since the population size will increase, there will be less variability within the sample. Therefore, the standard deviation will not increase. We do not know by how much because we do not know the current variability within the set.

Case 1#
- Every element of the set can be 22

Case 2#
- Every element in the set can be 26

IMO D

Does anyone have a different explanation or answer?
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The weights of a set of moving boxes on a truck have a mean of 22 poun 15 Mar 2022, 05:10
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The answer is B because if a set of terms have a SD and we want to add a new term in order to minimize the SD of that set then the new term must be closest to it's mean and closest to mean is mean itself. And if we want to increase it's SD then the term(s) must be farthest from it's mean.

Since, the two weights added are both equidistant i.e farther from it's mean weight, therefore, the SD will increase.
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The weights of a set of moving boxes on a truck have a mean of 22 poun 02 Jul 2023, 11:29
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gmatophobia
Can you please explain this problem ?

plus, let say SD in this problem is 4 then the new SD of the boxes still increase or remain the same ?
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The weights of a set of moving boxes on a truck have a mean of 22 poun 31 Aug 2024, 04:10
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gmatophobia

AnujL
gmatophobia
Can you please explain this problem ?

plus, let say SD in this problem is 4 then the new SD of the boxes still increase or remain the same ?
AnujL Standard deviation denotes how dispersed the data set is with respect to the mean.

In this question, we know that the mean weight of all the boxes is 22 pounds. The heavier box is 26 pounds (4 pounds above the mean) and the lighter box is 18 pounds (4 pounds below the mean). Hence after the two boxes that were added, the mean does not change and the mean of all the boxes is still 22 pounds.

Consider this - You've $22 with you, one friend gives you $4 and you lend $4 to another friend of yours. After both transactions, you will still have $22 with you.

Now back to the question - So after the two boxes are added the mean is still 22 pounds, however, we have added two data points which lie at some distance away from the mean. Hence the data set is now more dispersed and the SD increases.

Note:
1) The original value of standard deviation is not of any relevance to this question. So whether you take the original SD as 3, 4, or 2, the analysis and the behavior that the standard deviation increases remain the same.
2) We were able to arrive at the conclusion only because the value of the mean didn't change.
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­
I agree with the explanation and the approach taken to arrive at the correct answer. But I disagree with the 1st note which mentions that answer (that SD increases) is irrespective of the value of the original SD. Following is my reasoning:

If original SD is 3 then by a typical SD calculation formula, lets say sqrt (X/Y) = 3. Y is number of boxes (originally) and X is the numerator for a typical SD equation calculation.

Now 2 boxes of 18 and 26 pounds are added. So re-writing the SD equation

SD (revised) = SQRT [(X+ (18-22)^2 + (26-22)^2) / (Y+2)]
= SQRT [(X+32)/(Y+2)]

Now, lets try to prove that SD (revised) > SD (original), which means
=> [(X+32) / (Y+2)] > X/Y
=> X*Y + 32Y > X*Y + 2X
=> 16Y > X
=> X/Y <16
=> SD (original) < 4

This tells us that SD (revised) > SD (original) only when SD (original) <4. Thus, the answer depends on the SD(original) value and is not independent.­
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The weights of a set of moving boxes on a truck have a mean of 22 poun 01 Oct 2025, 08:02
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mean +/- 1 * SD covers 66.7% of the data of a sample space ( 22 + 3 = 25 and 22-3 = 19)

Now if you add 2 observations (18,26) which lie outside this area ( 19 to 25 ), then the deviation from mean is bound to increase.
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