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Standard deviation table

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Standard deviation table

by AbeNeedsAnswers » Mon Jul 03, 2017 8:28 pm

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C

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How do we calculate standard deviation?

---------------- Mon--Tues--Wed--Thu--
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

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

B
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by Jay@ManhattanReview » Mon Jul 03, 2017 11:05 pm
AbeNeedsAnswers wrote:How do we calculate standard deviation?

---------------- Mon--Tues--Wed--Thu--
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

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

B
The standard deviation of a data set is a measure of the deviations of the numbers in the data set w.r.t. their mean. More deviated (more distant) the numbers are from the mean, the more is their standard deviation and vice-versa.

Let's calculate the mean of the five companies and the deviations w.r.t. their mean.

'Dev-M' means the deviation of Monday and similarly for others...

-------- Mon--Tues--Wed--Thu--Mean--Dev-M--Dev-T--Dev-W--Dev-Th
Co A---45-----55----50----50-----50-------5---------5---------0--------0
Co B---10-----30----30----10-----20------10--------10-------10------10
Co C---34-----28----28----30-----30-------4---------2---------2--------0
Co D---39-----42----41----38-----40-------1---------2---------1--------2
Co E---50-----60----60----70-----60-------10--------0--------0--------10

We see that each value (10 each) of deviations for Company B is greater than that for companies A, C, and D. Also the two values for Company E are 0, while the other two (10 each) are equal, thus, SD would be the greatest for Company B.

In the GMAT, there is no need to compute the SD, mere analysis suffices.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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by Brent@GMATPrepNow » Tue Jul 04, 2017 5:51 am
Jay has done a great job solving the question.

I'd like to add that, for the purposes of the GMAT, it's sufficient to think of Standard Deviation as the Average Distance from the Mean. Here's what I mean:

Consider these two sets: Set A {7,9,10,14} and set B {1,8,13,18}
The mean of set A = 10 and the mean of set B = 10
How do the Standard Deviations compare? Well, since the numbers in set B deviate the more from the mean than do the numbers in set A, we can see that the standard deviation of set B must be greater than the standard deviation of set A.

Alternatively, let's examine the Average Distance from the Mean for each set.

Set A {7,9,10,14}
Mean = 10
7 is a distance of 3 from the mean of 10
9 is a distance of 1 from the mean of 10
10 is a distance of 0 from the mean of 10
14 is a distance of 4 from the mean of 10
So, the average distance from the mean = (3+1+0+4)/4 = 2

B {1,8,13,18}
Mean = 10
1 is a distance of 9 from the mean of 10
8 is a distance of 2 from the mean of 10
13 is a distance of 3 from the mean of 10
18 is a distance of 8 from the mean of 10
So, the average distance from the mean = (9+2+3+8)/4 = 5.5

IMPORTANT: I'm not saying that the Standard Deviation of set A equals 2, and I'm not saying that the Standard Deviation of set B equals 5.5 (They are reasonably close however).

What I am saying is that the average distance from the mean can help us see that the standard deviation of set B must be greater than the standard deviation of set A.
More importantly, the average distance from the mean is a useful way to think of standard deviation. This model is a convenient way to handle most standard deviation questions on the GMAT.

Cheers,
Brent

Here are a few more practice questions where we can apply the concept of "average distance from the mean" as an approximation for Standard Deviation:

https://www.beatthegmat.com/standard-dev ... 74384.html
https://www.beatthegmat.com/standard-dev ... 69584.html
https://www.beatthegmat.com/range-and-sd-t89159.html
Brent Hanneson - Creator of GMATPrepNow.com
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by ceilidh.erickson » Tue Jul 04, 2017 7:20 am
AbeNeedsAnswers wrote:How do we calculate standard deviation?

---------------- Mon--Tues--Wed--Thu--
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

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

B
First, please always POST YOUR SOURCES! It's a copyright violation not to do so, and it's important for other students to know which sources are valuable.

Other posters have given great explanations, but we can simplify it even further: with questions like these, it's enough to ask "which list is the most spread out?"

The GMAT will never require you to actually calculate standard deviation. That would be impossible without a calculator (and lots of time!). Here are a few more example of SD questions, so you can practice thinking about the spread without calculating:
https://www.beatthegmat.com/standard-dev ... tml#680908
https://www.beatthegmat.com/call-for-hel ... tml#545420
https://www.beatthegmat.com/standard-dev ... tml#724642
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by Matt@VeritasPrep » Wed Jul 05, 2017 12:56 am
ceilidh.erickson wrote:It's a copyright violation not to do so
Or, might we say, a copywrong?

(I'll show myself out ...)
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by ceilidh.erickson » Sun Jul 16, 2017 1:15 pm
Matt@VeritasPrep wrote:
ceilidh.erickson wrote:It's a copyright violation not to do so
Or, might we say, a copywrong?

(I'll show myself out ...)
groooooan! ;)
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Harvard Graduate School of Education
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Re: Standard deviation table

by [email protected] » Mon Apr 19, 2021 8:21 pm
Hi All,

While this question gives us a table full of data, we’re ultimately asked to think about which of the 5 Companies has the highest Standard Deviation in its data – and the GMAT will NEVER actually ask you to calculate S.D. Understanding the basic concepts behind S.D. are necessary though.

In terms of S.D. on the GMAT, the ‘closer’ a group of numbers is, the smaller the S.D; the more ‘spread out’ a group of numbers is, the higher the S.D. As such, you can answer this question with just a bit of Arithmetic and noting how the groups of numbers compare with one another.

To start, let’s look for groups of numbers that are close together (since those groups would have lower S.D.s and we can quickly eliminate them). Both Company C and Company D both clearly have the two closest groups. Eliminate Answers C and D.

With the 3 remaining groups, notice how Company A and Company E both revolve around a ‘central’ Average. Company A has two 50s, a 45 and a 55 – so the average is 50 and two of the terms differ by just 5 each. Company E has two 60s, a 50 and a 70 – so the average is 60 and two of the terms differ by 10 each. Thus, Company E is far more ‘spread out’ that group A is. Eliminate Answer A.

Company B has two 10s and two 30s, meaning that ALL FOUR terms differ from the Average by 10. That’s a far more spread-out group than the numbers in Company E.

Final Answer: B

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