PLA 6: Z - SCORES
KATE BREWER
So. Z-scores are going to come in handy in a raging argument between a friend over
whether cupcakes or muffins are more delicious, and thus more popular. You think
cupcakes are the obvious winner. Data was collected from two different scales, with
the items pertaining to either cupcakes or muffins. You realize, though, that after
getting your scores compiled you have no idea who wins loving their treat more since
it was on completely different size scales. But because you have taken a statistics
course from the most badass professor, you know just what to do to compare the two
and know with certainty which baked treat is king.
:::::::::::::: CUP CAKE STATS :::::::::::::
Mean: 16
SD: 2.1
You: 23
::::::::::::::: MUFFIN STATS :::::::::::::::
Mean: 42
SD: 7.8
You: 51
You know that all you need are your values for the mean, standard deviation, and
your individual scores. Once you have your data from your two scales, you need to
calculate your z-scores to find out who is right.
CUPCAKES:
MUFFINS:
(23−16)
2.1
(51−42)
7.8
= 3.33
= 1.15
Now that you have your z-scores, you can show off your
statistical knowledge to your friend. With these numbers,
you can tell them just where on a distribution your raw
scores lie, as well as how they compare to each other. So,
how do they compare? You proudly announce that you
unequivocally love cupcakes more than your friend loves
muffins. How do you know? You know because your zscore is 3.33, which is considerably beyond 2 standard
deviations from the mean, making you an extreme
cupcake lover. Your friend, as much as they may enjoy
their muffin, is only barely over 1 standard deviation from
the mean, so they are not an extreme muffin lover.