can you help me with a gr.7 math question?

Question

here's the question:
a teacher records the test marks of 25 students and calculates the class mean to be 72. jean-pierre finds out that his mark of 86 was recorded incorrectly as 36. what will the corrected class mean be?
i checked the answer key and it says the new class mean is 74, but i dont get how they got 74, so can you show me how you got 74, or you can show me how you did it and what you get so i'll know what went wrong and how i should do it. thank you!!! (and by the way, if you dont know what i'm talking about, then get lost)

Answer 1

Let x be the corrected class mean.

Balance by the total score:

25(72) + 50 = 25x

x = 74

Answer 2

Well first, the mean is found by adding all the students' scores and dividing by the number of students. It's an average. So the total number of the original count would have been x/25=72, which comes out to 72 * 25 = x and x is 1800. So if Jean-pierre had an 86 rather than a 36, the teacher would not have added in the extra 50 points. 1800 + 50 = 1850, of course. Then you simply divide by your total number of students again: 1850/25=74. You don't even need to know what every other student's score was, only the difference between his mismarked score and the actual score, which was an unaccounted for 50.

Answer 3

For the class average to be 72, the total of all the grades was 72*25=1800 changing the 36 to 86 adds 50 points so the real total is 1850. 1850/25=74

Answer 4

86 - 36 = 50
The marking was considered with 50 marks less.
Taking his mark as 36, the total number of marks scored by the class is:
25*72 = 1800
Now consider the missing 50 marks
1800 + 50 = 1850
New (and correct) mean = 1850/25
= 74

Answer 5

The easiest way to do this is to work out the sum of the marks with the incorrect score and then work out the correct sum of marks and then divide it to get the correct sum

Incorrect mean = 72
Therefore sum of incorrect marks = 72*25 =1800

Now we know that this score is actually too low. This should be 50 marks higher (86-36=50)

Therefore correct sum of marks = 1800 + 50 = 1850

Now we can divide to get the mean of 74 (1850/ 25=74)

Answer 6

incorrect mean=72
incorrect total=72*25=1800
less incorrect marks of jean pierre=36
=1764
add the correct marks 86 of jean pierre
correct total=1850
correct mean=1850/25=74

Answer 7

all the points togehter is 25 * 72 =288
without thew wrong 36 this is 288-36=252
with the new correct anser 252 + 86 = 3andosotething
so the new mean is (252 + 86)/25

Answer 8

m = (25*72 - 36 + 86)/25
m = (25*72 + 50)/25
m = 72 + 2
m = 74