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Math Expert V
Joined: 02 Sep 2009
Posts: 59720
The table above shows the number of packages shipped daily by each of  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:28) correct 25% (01:41) wrong based on 1814 sessions

### HideShow timer Statistics The table above shows the number of packages shipped daily by each of the five companies during a 4-day period. The standard deviation of the numbers of packages shipped daily during the period was greatest for which of the five companies?

A) A
B) B
C) C
D) D
E) E

Attachment: 2016-06-17_1615.png [ 26.43 KiB | Viewed 25339 times ]

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Target Test Prep Representative V
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Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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Bunuel wrote: The table above shows the number of packages shipped daily by each of the five companies during a 4-day period. The standard deviation of the numbers of packages shipped daily during the period was greatest for which of the five companies?

A) A
B) B
C) C
D) D
E) E

We are given the number of packages shipped by 5 companies. Let’s list those below:

Company A: 45 ,55, 50, 50

Company B: 10, 30, 30, 10

Company C: 34, 28, 28, 30

Company D: 39, 42, 41, 38

Company E: 50, 60, 60, 70

We may recall the the standard deviation represents how far the data points are from the mean. It’s not necessary to calculate the standard deviations of any of the data sets. Let’s “eyeball” the list instead. We see that the data points of Companies B and E are most spread apart. Thus, the largest standard deviation will come from either Company B or Company E.

Let’s calculate the mean (arithmetic average) for Company B and E.

Mean of Company B = (10 + 30 + 30 + 10)/4 = 80/4 = 20

For Company B, we see that the distances of the data points are 10, 10, 10, and 10, respectively, from the mean. (Note that we don’t care about the + or - signs of those distances.)

Mean of Company E = (50 + 60 + 60 + 70)/4 = 240/4 = 60

We see that the distances of the data points are 10, 0, 0, and 10, respectively, from the mean.

Thus, company B has a greater standard deviation than company E and hence the greatest standard deviation of the 5 companies.

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Manager  Joined: 19 Dec 2015
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Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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10
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Company A : 45, 50, 50, 55. Mean = 50. Distance of each element from the mean = 5, 0, 0 , 5.
Company B : 10, 10, 30, 30. Mean = 20. Distance of each element from the mean = 10, 10, 10, 10
Company C : 28, 28, 30, 34. Mean = 30. Distance of each element from the mean = 2, 2, 2, 2
Company D : 38, 39, 41, 42. Mean = 40. Distance of each element from the mean = 2, 1, 1, 2
Company E : 50, 60, 60, 70. Mean = 60. Distance of each element from the mean = 10, 0, 0, 10.

From the data above, we can clearly see that the elements in B are most widely spread. And thus has the highest standard deviation. Hence B.
##### General Discussion
Current Student B
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Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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1
The numbers in A, C, D are close.

B vs E:

For E, two of the deviations are zero
For B, all deviations are 10

So B is the clear choice.
Manager  B
Joined: 08 Jun 2017
Posts: 53
The table above shows the number of packages shipped daily by each of  [#permalink]

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Is nt there something like The highest std in a set will be something with the highest range. In that case isnt E the answer ? I know the Std will anyway be less in E . But how come this theory is contradicting. Bunuel i used the same logic that u had given for ur statistics qns in ur signature. Kindly explain. !!!

Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4473
Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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Asac123 wrote:
Is nt there something like The highest std in a set will be something with the highest range. In that case isnt E the answer ? I know the Std will anyway be less in E . But how come this theory is contradicting. Bunuel i used the same logic that u had given for ur statistics qns in ur signature. Kindly explain. !!!

Dear Asac123,

I'm happy to respond. :-)

Standard Deviation on the GMAT
Give particular attention to the section "Rough and ready facts about standard deviation."

For this question, (B) & (E) both have a range of 20, a larger range than the others, so let's eliminate the other three and discuss these two.

Standard deviation is, we might say, a measure of the "typical" distance between the data points in a set and the mean of the set.

In (E), the mean is 60. Two of the data points are at 60, so they have a deviation of zero, and two are 10 away from 60, so they have deviations of +10 and -10. The set of deviations is {-10, 0, 0, 10}. Ignoring positive/negative, what's the typical size of those four numbers? Hard to say. It would be something between 0 and 10.

Now, look at (B). The mean is 20, and every single data point is exactly a distance of 10 from this mean of 20. If every data point is the same distance from the mean, that distance has to be the S.D. For (B), S.D. = 10.

Since the S.D. of (B) is equal to 10 and the S.D. of (E) would be less than 10, we know that (B) has to have the biggest.

Suppose we want the exact value of the S.D. of (E). This is more than you need to know for the GMAT, but what you would do is square those deviations, add them up, average those squared values, and then take a square root of that average.
list of deviations = {-10, 0, 0, 10}
list of squared deviations = {100, 0, 0, 100}
average of squared deviations = 50
$$S.D. = \sigma = \sqrt{50} = 5\sqrt{2} = 7.071$$

Does all this make sense?
Mike :-)
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Joined: 08 Jun 2017
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Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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mikemcgarry wrote:
Asac123 wrote:
Is nt there something like The highest std in a set will be something with the highest range. In that case isnt E the answer ? I know the Std will anyway be less in E . But how come this theory is contradicting. Bunuel i used the same logic that u had given for ur statistics qns in ur signature. Kindly explain. !!!

Dear Asac123,

I'm happy to respond. :-)

Standard Deviation on the GMAT
Give particular attention to the section "Rough and ready facts about standard deviation."

For this question, (B) & (E) both have a range of 20, a larger range than the others, so let's eliminate the other three and discuss these two.

Standard deviation is, we might say, a measure of the "typical" distance between the data points in a set and the mean of the set.

In (E), the mean is 60. Two of the data points are at 60, so they have a deviation of zero, and two are 10 away from 60, so they have deviations of +10 and -10. The set of deviations is {-10, 0, 0, 10}. Ignoring positive/negative, what's the typical size of those four numbers? Hard to say. It would be something between 0 and 10.

Now, look at (B). The mean is 20, and every single data point is exactly a distance of 10 from this mean of 20. If every data point is the same distance from the mean, that distance has to be the S.D. For (B), S.D. = 10.

Since the S.D. of (B) is equal to 10 and the S.D. of (E) would be less than 10, we know that (B) has to have the biggest.

Suppose we want the exact value of the S.D. of (E). This is more than you need to know for the GMAT, but what you would do is square those deviations, add them up, average those squared values, and then take a square root of that average.
list of deviations = {-10, 0, 0, 10}
list of squared deviations = {100, 0, 0, 100}
average of squared deviations = 50
$$S.D. = \sigma = \sqrt{50} = 5\sqrt{2} = 7.071$$

Does all this make sense?
Mike :-)

Thanks Mike i understand that but if we take the range concept then wouldnt E be the answer
Manager  B
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Concentration: Finance, Technology
GMAT 1: 650 Q47 V34 GPA: 3.41
Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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You don't need to calculate or solve this one, observe with logic you will be able to eliminate most of the choices.
Intern  B
Joined: 11 Sep 2013
Posts: 20
Schools: CBS '19
Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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1
In order to answer this question, one has to know the concept of Standard Deviation (SD).
Standard Deviation (SD) is a statistical concept that measures the amount of variation or dispersion of a set of data points.
In other words, SD measures the distance between the MEAN (AVERAGE) of a given set and each and every DATA POINT in a given set. (MEAN - DATA POINT)
Simply, SD tells you how far or how close is the MEAN (AVERAGE) of a given set from each and every DATA POINT in a given set.
SD is moody and it can be HIGH or it can be LOW .
SD is High when the MEAN is far away from each and every DATA POINT in a given set.
SD is Low when the MEAN is close to each and every DATA POINT in a given set.

The question asks for the GREATEST (HIGHEST ) SD for the number of packages shipped daily at five different companies.
The first step is to find the MEAN for each and every company and then find the highest SD by subtracting the MEAN with each and every DATA POINT
As you can see from the table the figures are "very friendly" and if you are experienced you can do mental math here.

Company A:
DATA POINTS: 45 55 50 50
MEAN: 50
SD: 5 5 0 0

Company B:
DATA POINTS: 10 30 30 10
MEAN: 20
SD: 10 10 10 10

Company C:
DATA POINT: 34 28 28 30
MEAN: 30
SD 4 2 2 0

Company D:
DATA POINTS: 39 42 41 38
MEAN: 40
SD: 1 2 1 2

Company E:
DATA POINTS: 50 60 60 70
MEAN: 60
SD 10 0 0 10

As you can see SD at company B is the highest for each and every DATA POINT (10 10 10 10). Hence, the correct answer is B.
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Re: The table above shows the number of packages shipped daily by each of  [#permalink]

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