Question 1204325
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Answer:  <font color=red size=4>87</font>


Explanation


The other tutors have great approaches.
I'll use a method that doesn't involve algebra.


Let's assume the first 5 tests had scores of 97 since this is the average we want.
The 6th test would have a score of 97-12 = 85.


The 6 scores are: 97,97,97,97,97,85


To get the average we add up the values and divide by the sample size (the number of items in the set).
Add the scores: 97+97+97+97+97+85 = 570
Divide by 6 to get: 570/6 = 95


The average we get (95) is smaller than the average we want (97).


Let's bump each grade up by 1 point and repeat the process
scores = 98,98,98,98,98,86
average = (98+98+98+98+98+86)/6 = 576/6 = 96
We're getting closer to the goal.


Let's bump each grade up by 1 point and repeat the process
scores = 99,99,99,99,99,87
average = (99+99+99+99+99+87)/6 = 582/6 = 97
We finally land on the average we want.


Therefore, Bobo's score on the 6th test was 87.


This trial-and-error process didn't take too long. 
However, we might not be so lucky in other problems. 
That's why the algebraic approach is often more efficient.


If you are familiar and confident with algebraic notation, then check out this lesson
<a href = "https://www.algebra.com/algebra/homework/Probability-and-statistics/statistics-transformations1.lesson">https://www.algebra.com/algebra/homework/Probability-and-statistics/statistics-transformations1.lesson</a>
In that lesson I prove that adding a certain value k to each item in a set would increase the mean by k.
This helps explain why the mean increased by 1 each time we bumped the grades up by 1.
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