Powerprep I, pr. 16

[irs031]

In a survey 100 travel agents each ranked Airlines A, B and C in order of preference. Each of the 100 travel agents also rated the three airlines in five categories on a scale of 1 to 10, with 10 being the best rating.

Average rating
Category Airline
A ; B ; C
Convenience 5.1 8 4.3
Friendliness 5 5.5 5.4
Price 5 6.4 3.5
Promptness 6.5 6.9 4.1
Reliability 7.8 7.5 4.9


Distribution of rankings:
BAC : 34%
BCA: 20%
CAB: 20%
ABC: 18%
ACB: 6%
CBA: 2%
(in the original problem this is a pie chart)
(BAC means B first, A second, C third; BCA= B first, C second, A third, etc)


If each of the average ratings was the arithmetic mean of the ratings given by the 100 travel agents, approximately how much greater was the total of the ratings given to all 3 airlines for reliability than for promptness
A) 25 B)50 C)125 D)250 E)500




I have a little bit of trouble understanding what the question is asking me to do here. The way I understand it that I need to sum up the ratings for promptness and reliability and compute their difference.

I have most difficulty understanding this sentence "If each of the average ratings was the arithmetic mean of the ratings given by the 100 travel agents"

6.5+6.9+4.1=17.5
7.8+7.5+4.9=20.2
The difference here 2.7 is not among the answer choices.


Thanks for you help.

[tommywallach]

Average rating
Category Airline
A ; B ; C
Convenience 5.1 8 4.3
Friendliness 5 5.5 5.4
Price 5 6.4 3.5
Promptness 6.5 6.9 4.1
Reliability 7.8 7.5 4.9


If each of the average ratings was the arithmetic mean of the ratings given by the 100 travel agents, approximately how much greater was the total of the ratings given to all 3 airlines for reliability than for promptness
A) 25 B)50 C)125 D)250 E)500

Yes, you are misunderstanding. They want the total of ALL the ratings. Remember, each of these ratings was calculated by asking 100 people. So we're adding up all 100.

Sum = Average/# of people

So for promptness, we have three scores, each of which represents the average of 100 people. Using the average equation above, we get:

Sum = 6.5/100
Sum = 6.9/100
Sum 4.1/100

Our three sums are 650, 690, and 410, adding up to 1750.

For reliability, our three calculations are:

Sum = 7.8/100
Sum = 7.5/100
Sum = 4.9/100

Our three sums are 780, 750, and 490. These add up to 2020.

The difference between 1750 and 2020 is approximately 250.

-t