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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Probus