If the raw score is 62, the mean is 58 with a standard deviation of 8, what is the Z score?

Question

 An individual receives a raw score of 62 on a national standardized test. Given that the mean & standardized deviation of the test were 58 and 8, respectively, what is the individual's Z-score?

Answer 1

Hi, Paula!

 

I know that you asked this a few days ago and have two excellent answers above, but I just wanted to add in my two cents! :)  The z-score of any raw data point tells you exactly how many standard deviations away from the mean an individual data point is.  In high school, you learn about standard deviations in .5 increments, how the standard deviations look on a bell curve/normal distribution, and how to find the distance away from the mean that a specific data point is when it falls 1, 1.5, 2, etc. standard deviations away from the mean.  Z-scores are a way to calculate exactly how far a data point is from the mean, even when the data point doesn't fall 1 or 1.5 or 2 standard deviations away.  For instance, if a raw data point is 2.35 standard deviations away from the mean, you wouldn't be able to get that specific by looking at a normal distribution graph and counting standard deviations in .5 increments.  You need an actual calculation method (as given in Mark's answer above).

 

I hope that this helps you understand what z-scores are a little better!  If you need more help, feel free to contact me!  I work/live in Verona, NY, right around the corner from Vernon.

 

- Patty

Answer 2

For this question, we will use the formula:

Z = (X- μ)/σ

where X is our raw score, μ is our Mean, and σ is our standard dev.
From the information we have:
Raw score = 62
Mean = 58
Standard Dev. = 8
now simply plug in the information and we have!

Z = (62 - 58)/8
z= (4)/8
z = .5

Answer 3

z-score = (raw score - mean)/(standard deviation)

 

              = (62 - 58)/8 = 4/8 = 0.5