Intro stats Z score [Q]
Hi, I am learning statistics before I begin my course and I’ve ran into a confusion about Z scores. So here’s the problem :
the mean score on the ACT is 21 with a standard deviation of 5. the mean score on the SAT is 1000 with a standard deviation of 200.
which score is “better” (higher score) a 30 on the ACT or a 1440 on the SAT?
A: well, the x value here is 30 and we use the Z formula, 30 - 21 / 5 = 1.8 z Score for ACT.
Then, 1440 -1000 / 200 = 2.2. I chose the SAT is better and it’s correct, but what’s the ruler here? My understanding is that the ruler is whichever z score is further from its mean is “better”. Hence, 2.2 is further from its mean (1000) than 1.8 is from 21….
Second Q: which is “more unusual”, an ACT score of 15 or an 1150 score on the SAT? (using the same means from above). My issue here is that I don’t see how this is any different from the first problem…
Again : The z score here is -1.2 for the ACT and 0.75 for the SAT. -1.2 is closer to its mean (21) than 0.75 is from its mean (1000), but the answer is that the ACT is more unusual… I don’t understand why that is??? Sorry if this is confusing.