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At the end of each year, the Harcar Corporation assigns a rating to ea

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At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   Updated on: 10 Nov 2023, 01:21
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Question Stats:

42% (02:42) correct 58% (02:35) wrong based on 153 sessions
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At the end of each year, the Harcar Corporation assigns a rating to each member of its sales staff. The sales ratings are based on the mean (μ) and standard deviation (σ) for the individual sales totals for the year. The rating is computed by applying the following formula and then rounding the result to the nearest integer.

\(Individual rating=\frac{individual total-μ}{σ}\)

Sales staff are considered for promotion if their rating is 3. The graph shows the ratings for the entire sales staff for the years 2009, 2010, and 2011.

1. The graph the claim that the sales staff had the fewest members in 2010.

2. The graph the claim that, as a group, the staff’s total sales were highest in 2011.


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Dropdown 1: Refutes Dropdown 2: Nor supports neither refute

Originally posted by Sajjad1994 on 15 Jun 2020, 11:14.
Last edited by BottomJee on 10 Nov 2023, 01:21, edited 2 times in total.
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   26 Mar 2024, 02:09
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­A cursory glance at this question may make this question appear too difficult – the definition of standard mean and deviation and the calculation of rating from these measures. But once you truly understand the dataset, you will be able to answer this question with confidence.

As you watch the solution, get answers to the following question:
  1. For question 1, did you answer through visualization without any calculations or did you compute the sum?
  2. For question 2, were you able to reason out why the data presented is not sufficient to answer the question asked?



If you answer to both questions is YES, then you have demonstrated the skills required to answer this GI question. If any of the answers is NO, then you should work on the skill of ‘owning the dataset’.
Happy Learning.
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   15 Jun 2020, 11:48
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1. The graph_____________the claim that the sales staff had the fewest members in 2010.

For sales to be lowest in 2010, there would have to be least or no promotions in 2010, which would depend on the ratings from 2009.
We can infer from the chart, that the the fewest members would have been in 2011, since the number with rating was even lower in 2010 and lowest in 2011 for a rating of 3.

So the graph refutes the claim.

Answer B.

2.The graph_____________the claim that, as a group, the staff’s total sales were highest in 2011.

I am choosing Nor supports neither refute, since no inference can be made, to the claim that the staff’s total sales were highest in 2011.


Answer C.
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   16 Jun 2020, 09:44
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1)B,since for fewest members in a particular year,it depends on the number of promotions,which ultimately depend on the sales,but if we see the graph to know the number of people who achieved 3 rating,we would find that the number of people who get 3 is continuously decreasing so fewest members would be in 2011 since in 2010 less people got 3 rating than the number who got in 2009

2)C,Since no inferences can be made just on seeing the ratings because we don't know the mean and standard deviations ,through which if put all these things in the given formula to compute the total sales in a year

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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   18 Jun 2020, 20:32
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2010 : graph is higher than other 2 graphs in ratings ( -3,-2,-1,1,2) and at 2nd top ( 0 and 3)
It means staff members were not lowest in 2010 by summing up all staff members
>>REFUTES

2011( lowest in all ratings in graph)
We don’t know if only few staff members in 2011 with higher rating could have high revenue that could be higher than overall sum of stff members with ratings over other years
>> Nor supports neither refute
Approach2:

Case1:
Say staff sales numbers= 10,20,30,40,50,60,70$; mean= 40
Standard deviation = sqrt (30)^2 + 20^2+10^2+0 +10^2+20^2+30^2)/7= 20

Rating 3= (individual total ( 70)- 40(mean))/(20) = 1.5
Rating2: 60-40/20 = 1
Rating1= 0.5
Rating0 = 0
Rating -1= -0.5
Rating -2= -1
Rating -3= -1.5

Case2:
Above ratings could be achieved if we choose the numbers
100,200,300,400,500,600,700$; mean= 400
Standard deviation = 200
Rating 3= (individual total ( 700)- 400(mean))/(200) = 1.5


If we need to calculate for different years, without any individual sales figure we can not determine total sales

>> Nor supports neither refute
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   30 Jun 2020, 07:38
Case1- Option B: Refutes

The graph for 2011 has highest number (members) with ratings at -3,-2,-1,1,2 and second highest at 0 and 3, which no where claims that the graph had the fewest members in the year 2011.
Therefore refutes the claim.

Case2- Option C : Nor supports neither refute
There hasn't been any mention of the sales figure or any correlation with the data provided. Therefore it can't be infered that the sales were highest in 2011.
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   05 Apr 2021, 03:30
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Official Explanation

RO1

The graph indicates that there were a greater number of 2010 sales members than 2011 sales members in every sales rating category. Thus, there must have been more sales members in 2010 than in 2011, refuting the claim that the sales staff had the fewest members in 2010.

The correct answer is refutes.

RO2

Each individual's sales total could be calculated from his or her rating by the formula individual total = (individual rating) + if values for and were known. These values are, however, not known. Thus, it is impossible to determine the individual sales totals and, therefore, impossible to determine the staff's total sales which may or may not have been highest in 2011.

The correct answer is neither supports nor refutes.
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink] New post   23 Mar 2024, 08:18
Hi GMATCoachBen, Could you please help solve this question. It seems a bit complicated to understand
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Re: At the end of each year, the Harcar Corporation assigns a rating to ea [#permalink]
23 Mar 2024, 08:18
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