Which test did Peter do better relative to the rest of the class?

Question

On Peter's first math test he scored 78. The mean and standard deviation for the class were 75 and 12 respectively. On his second math test, Peter scored 84. The mean and deviation for the class were 72 and 18 respectively. On which test did Peter do better relative to the rest of the class?

Answer 1

To do these types of problems l like to use the z-score formula. The formula will assist you in getting the P-value, which will show the percentage of people Peter scored better than.  

 

The formula is z = (X - μ) / σ

X=the test he scored

Mu=the class average

Standard Deviation

 

Test 1:

Z= (78-75)/12

Z= .25

If you look up the number in the Z chart you will find that the P-Value is .5987

This means that he did better than roughly 60% of his classmates

 

Test 2:

Z= (84-72)/18

Z= .67

If you look at the chart for the (.67), you will see that the P-Value is .7486

This means that he did better than roughly 75% of his classmates

 

Judging by the P-Values it would seem that in test 2 he did much better than the rest of the class than test 1.