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# A student's average (arithmetic mean) test score on 4 tests

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Manager
Joined: 10 Apr 2018
Posts: 180
Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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15 Aug 2018, 15:07
Hi,

For questions like these we have a very quick method called deviation method.
Fisrt, Average is nothing but adding up everything and dividing it equally.

Let me take a moment to explain how this method works.
Say we are told average weight of a group of 7 persons is 60 Kg. If new person who weighs 76 Kgs joins the group, what will be the new average?

There are 7 people in the group initially and 1 person joins the group. And this new person's weight is 76Kgs.
Now just for a moment assume that the new persons weight was 60kg, which is the same as the initial average .Then if new persons weight was 60 Kgs then the average would remain unchanged. But the new persons weight is 76 Kgs which is 16 kgs more than 60 Kgs.
Average is dividing the weight equally among all people. So this deviation of 16kgs would be divided equally among 8 people of the group.

New Avg= 60 +16/2
New Avg= 62
In general:
New avg= Assumed value +or- (deviation/n+1)

let's take one more Say we were told that 4 Cell Phones were sold at average price of 1200 \$, if 5 cell phone is sold at 1100\$ what is the new average?

Here if the 5th Cell phone were to sell at 1200\$ the new average would have been the same.

So lets assume the price at which fifth cellphone is sold as 1200. Now since the fifth Cellphone is sold at 1100 which is \$ 100 less than the assumed price , So this deviation of - \$100 would be divided equally among the 5 Cellphones in the group.
hence
new avge= 1200- (100/5)
new avg= 1200-20
new avg=1180/-

So in general ,
New Avg= Assumed new value +or- (deviation)/n+1

No lets try using this in above question,

Lets say the student scores 78 on the fifth test. Now since the new average is increasing the deviation must have been added to the assumed value.lets say the deviation is x
So
80=78+(deviation/5)
80=78+x/5
2=x/5
so x=10
This means deviation 10 from assumed 78 Hence the score on 5 Test must have been 88.

Probus
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Joined: 11 Sep 2015
Posts: 3341
Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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28 Aug 2018, 13:54
Top Contributor
Bunuel wrote:
A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?

(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

My first approach would be identical to the ones shown above. However, we can also solve the question using the weighted averages formula:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

We want the TOTAL average to equal 80
4/5 of the 5 scores have an average of 78
Let x = average of the 1 remaining test, which is worth 1/5 of the total average.

We get: 80 = (4/5)(78) + (1/5)(x)
Multiply both sides by 5 to get: 400 = 312 + x
Solve: x = 88

Cheers,
Brent
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Joined: 28 Apr 2016
Posts: 42
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: A student's average (arithmetic mean) test score on 4 tests  [#permalink]

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30 Aug 2018, 13:11
While there have already been some efficient approaches to this question posted in this thread, I thought that I would also show how this question can be solved quickly using the weighted average mapping strategy (the link contains a list of questions that can be used to practice using the weighted average mapping strategy, also knows as the tug of war).

In general, the weighted average mapping strategy can be used to solve problems like this, where 1 more item is being added to a group. One weight will be the number in the original group (4 in this question), and the other weight will be 1, the size of the "group" of one being added; these are shown above the line in the diagram below. We know the average of the original group (78) and the final weighted average (80), so we can fill these in below the line in the diagram. We need to solve for the "average" of the group of 1 (which will be the score on the 5th test) by making the ratio of the weights equal to the ratio of the distances. The ratio of the weights is 4:1, and the smaller distance is 2, so the larger distance must be 8. Thus, the score of the 5th test is 80+8 = 88.

When I drew the diagram above by hand, I timed myself and found that it took me just 12 seconds. Please let me know if you have any questions, or if you want me to post a video solution!
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Re: A student's average (arithmetic mean) test score on 4 tests &nbs [#permalink] 30 Aug 2018, 13:11

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