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# ps (m02q28)

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VP
Joined: 09 Jul 2007
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15 Nov 2007, 17:18
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The following table shows results of a quality inspection of a lot of 15 mirrors.

Defects Frequency
_0________ 6
_1________ 1
_2________ 4
_3 ________3
_4 ________1

The difference between the median defects and the average defects in the sample checked is between:

(A) -1 and 0
(B) 0 and 0.5
(C) 0.5 and 1
(D) 1 and 1.5
(E) 1.5 and 2

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions
Manager
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02 Mar 2010, 22:55
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Ravshonbek wrote:
The following table shows results of a quality inspection of a lot of 15 mirrors.

Defects Frequency
_0________ 6
_1________ 1
_2________ 4
_3 ________3
_4 ________1

The difference between the median defects and the average defects in the sample checked is between:

0
0 and 0.5
0.5 and 1
1 and 1.5
1.5 and 2

the arrangement would be as under

0 0 0 0 0 0 1 2 2 2 2 3 3 3 4

here the median is 2

The mean is 1.47 (22/15)

the answer is 2-1.47 = 0.53 (C)
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Manager
Joined: 11 May 2007
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15 Nov 2007, 20:06
3
KUDOS
Ravshonbek wrote:
The following table shows results of a quality inspection of a lot of 15 mirrors.

Defects Frequency
_0________ 6
_1________ 1
_2________ 4
_3 ________3
_4 ________1

The difference between the median defects and the average defects in the sample checked is between:

0
0 and 0.5
0.5 and 1
1 and 1.5
1.5 and 2

I am missing something here:

Median - 2
Mean - {0(6) + 1(1) + 2 (4) + 3 (3) + 4 (1)}/15 = 1.47
Difference b/c Median & Avg: 2 - 1.47 = 0.53

What is the OA?
Manager
Joined: 10 Dec 2006
Posts: 90
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16 Nov 2007, 22:07
1
KUDOS
A similar problem exists in GMAT club challenge 24 (question 26). Check out its explanation.

rakesh22 wrote:
GMATBLACKBELT wrote:
yogachgolf wrote:
Ravshonbek wrote:
The following table shows results of a quality inspection of a lot of 15 mirrors.

Defects Frequency
_0________ 6
_1________ 1
_2________ 4
_3 ________3
_4 ________1

The difference between the median defects and the average defects in the sample checked is between:

0
0 and 0.5
0.5 and 1
1 and 1.5
1.5 and 2

I am missing something here:

Median - 2
Mean - {0(6) + 1(1) + 2 (4) + 3 (3) + 4 (1)}/15 = 1.47
Difference b/c Median & Avg: 2 - 1.47 = 0.53

What is the OA?

I get the same

I too get the same, 0.53. We are not concerned with the sample size, but, only with the number of defects in the given sample.
Intern
Joined: 14 Sep 2010
Posts: 7
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25 Sep 2010, 00:13
1
KUDOS
GaryDunn wrote:
cnrnld wrote:
15 mirrors, but with a total number of 22 as defective?

I don't understand this:(

It implies that the company is measuring more than one type of defect.

Its 22 defects in 15 lots of 15 mirrors each. I Got C.
Manager
Joined: 18 Jan 2012
Posts: 51
Location: United States
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28 Sep 2012, 06:51
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Amardeep Sharma wrote:
B = 0 and 0.5

In the sample of 15 numbers, median will be (7th + 8th)/2, in this case 7th number is 1 and 8th number is 2 so median = 1.5

Average of the number is addition of all the numbers of defects divided by 15 = 3/5,

so Median - avg = 9/10, which lies between 0 and 0.5

Amar

Whoah there tiger.
Median of 15 terms is the 8th term, not the average of 7th and 8th.
Median is 2.

Mean of any set which consists of n odd integers is Quotient (n/2) + 1 = 15/2 + 1 = 8th term
Mean of any set which consists of n even integers is the average of the "n"th and "n+1" term

For any arithmetic progression, Mean = Median = Average = Average of first and last term

Back to the problem..............
Average = 22/15, which is a little bit less than 1.5 (Why ? Because 1.5 x 1.5 = 225. Knowledge of squares comes in handy here. The GMAT never asks you to do busy work.
Always remember that !!! )
Difference = 2 - (a term that is a little bit less than 1.5) = A term that is a little bit more than 0.5
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Director
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Location: Indonesia
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15 Nov 2007, 17:24
B = 0 and 0.5

In the sample of 15 numbers, median will be (7th + 8th)/2, in this case 7th number is 1 and 8th number is 2 so median = 1.5

Average of the number is addition of all the numbers of defects divided by 15 = 3/5,

so Median - avg = 9/10, which lies between 0 and 0.5

Amar
VP
Joined: 09 Jul 2007
Posts: 1100
Location: London
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15 Nov 2007, 17:36
i think i cannot read the table. where are the lots of 15 mirrors. how are they represented in the table?

thanks
Manager
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15 Nov 2007, 17:40
Amardeep Sharma wrote:
B = 0 and 0.5

In the sample of 15 numbers, median will be (7th + 8th)/2, in this case 7th number is 1 and 8th number is 2 so median = 1.5

Average of the number is addition of all the numbers of defects divided by 15 = 3/5,

so Median - avg = 9/10, which lies between 0 and 0.5

Amar

I did it the same way, but, and Im sure Im being a moron, why if there are an odd number of mirrors do we need to average two items - surely the 8th mirror is the median?
Director
Joined: 13 Dec 2006
Posts: 512
Location: Indonesia
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15 Nov 2007, 17:45
Yep, you are right and I am wrong... thnx for correcting me....

I dont know how I made that mistake, well as you got median as 2, rest will follow the same procedure

thanx once again

Amar
Manager
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15 Nov 2007, 23:33
GMATBLACKBELT wrote:
yogachgolf wrote:
Ravshonbek wrote:
The following table shows results of a quality inspection of a lot of 15 mirrors.

Defects Frequency
_0________ 6
_1________ 1
_2________ 4
_3 ________3
_4 ________1

The difference between the median defects and the average defects in the sample checked is between:

0
0 and 0.5
0.5 and 1
1 and 1.5
1.5 and 2

I am missing something here:

Median - 2
Mean - {0(6) + 1(1) + 2 (4) + 3 (3) + 4 (1)}/15 = 1.47
Difference b/c Median & Avg: 2 - 1.47 = 0.53

What is the OA?

I get the same

I too get the same, 0.53. We are not concerned with the sample size, but, only with the number of defects in the given sample.
Manager
Joined: 20 Sep 2006
Posts: 58
Followers: 1

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16 Nov 2007, 04:35
Difference between median & mean is 0.53, Ans. C)
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17 Nov 2007, 13:05
VP
Joined: 09 Jul 2007
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17 Nov 2007, 14:30
OA is C, thanks a million
Intern
Joined: 25 Aug 2010
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24 Sep 2010, 06:06
15 mirrors, but with a total number of 22 as defective?

I don't understand this:(
Senior Manager
Affiliations: Volunteer Operation Smile India, Creative Head of College IEEE branch (2009-10), Chief Editor College Magazine (2009), Finance Head College Magazine (2008)
Joined: 26 Jul 2010
Posts: 467
Location: India
WE2: Entrepreneur (E-commerce - The Laptop Skin Vault)
Concentration: Marketing, Entrepreneurship
GMAT 1: 710 Q49 V38
WE: Marketing (Other)
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24 Sep 2010, 06:33
Foiled by poor reasoning
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Intern
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24 Sep 2010, 08:11
cnrnld wrote:
15 mirrors, but with a total number of 22 as defective?

I don't understand this:(

It implies that the company is measuring more than one type of defect.
Intern
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

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14 Oct 2010, 08:57
GMATBLACKBELT wrote:
yogachgolf wrote:
Ravshonbek wrote:
The following table shows results of a quality inspection of a lot of 15 mirrors.

Defects Frequency
_0________ 6
_1________ 1
_2________ 4
_3 ________3
_4 ________1

The difference between the median defects and the average defects in the sample checked is between:

0
0 and 0.5
0.5 and 1
1 and 1.5
1.5 and 2

I am missing something here:

Median - 2
Mean - {0(6) + 1(1) + 2 (4) + 3 (3) + 4 (1)}/15 = 1.47
Difference b/c Median & Avg: 2 - 1.47 = 0.53

What is the OA?

I get the same

I also got the same thing.
Intern
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27 Sep 2013, 23:55
the median is 2
the avg is 22/15
so, median - avg = 2 - 22/15 = 8/15

hence answer is between 0.5 and 1.
C.
Senior Manager
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01 Oct 2013, 12:59
Median is 2 (take the middle number in the frequency)
The average is 22/15 which you do not have to calculate just state that it is less than 1.5 (logic because 22.5/15=1.5)! Lets say 1.4 to make the logic simplier.

Therefore, you have the difference 2-1.4: 0.6.

The difference is between 0.5 and 1. Answer C.
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Re: ps (m02q28)   [#permalink] 01 Oct 2013, 12:59
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# ps (m02q28)

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