Question

Who did better? Peter with a score of 92 in a test with mean 71 and standard deviation 15, OR Mary with a score 688 in a test with mean 493 and standard deviation 150

Answer 1

For these kind of prblems we have to calculate the Z scores.

Z score means the standard score which tells us that how far from the mean the data point is.

Z scores are basically used to compare results to a normal population. Suppose we have to compare two or more values to each other but all the values are calculated on a different base. So to calculate the relation between them we need a common base and that common base is the Z score.

Formula for Z score is :-

where ,

Z is the Standard score i.e z score

x is the observed value

u is the mean

is the standard deviation

Now calculate the Z score for both the persons and on the basis of that we can compare that who is better. Person having the higher Z score will be better.

For Peter :-

For Mary :-

As we can see that the Z scores of both Peter and Mary are approximately equal so we can say that relatively no one is better than another.

No one is better than other.