Question

The mean test score for a class was 70 points, with a standard deviation of 15 points. If I now add 10 points to everyone's test score:

a) What is the mean test score for the class after I add the 10 points to each score?

b) What is the standard deviation of the test scores for the class after I add the 10 points to each score?

Answer 1

well look at this example

65 70 and 75 are the 3 test scores the mean is 70

add 10 the each score you get

75, 80 and 85 what happens to the mean...?

(b) standard deviation measure the average spread of a score from the mean...

so if each score increases by x and the mean increases by x do you think the average spread will change..?

Answer 2

Each student's score increases by 10 but, I don't know what the classes mean score with the additional is because I don't know the number of scores. Unless the whole average for the whole class increases by 10. In that case, the mean class score would be 80?

No? But I have to give the actual number, so if no it would remain 15? How would I show that by working it out?

Answer 3

well look at the example... imagine a class of 3... what happens to the mean..?

65, 70 and 75 have a mean of 70

add 10 to each

75, 80, 85 so what is the new mean..?

Answer 4

80

Answer 5

great... so the number of students won't change the mean score... of you add 10 to all students the mean will increase by 10... as you just found...

Answer 6

So the new mean of the class would be 20?

Answer 7

and as far as standard deviation goes there is no change... as everything maintains its position in relation to the mean.

no the new mean score is 80

Answer 8

Oh shoot! That's what I meant. I just had 10 on the brain.

Answer 9

hope it helps

Answer 10

And the Standard Deviation would remain 15?