SOLUTION: Hello Could I please get some help with this problem. I am really confused on how to even get it started? A set of 50 data values has a mean of 15 and a variance of 36. Find

Question 663884: Hello
Could I please get some help with this problem. I am really confused on how to even get it started?
A set of 50 data values has a mean of 15 and a variance of 36. Find the standard score of a data value = 15
THanks
Found 2 solutions by Theo, solver91311:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
set of 50 data values.
mean = 15
variance = 36
standard score is the z score i presume.
the formula to derive a z score from a raw score (15 is a raw score) is:

z = (x - m) / sd
z is the z score
x is the raw score
m is the mean
sd is the standard deviation.

you are given a mean of 15 and a raw score of 15 and a variance of 36

the standard deviation is the square root of the variance, so your standard deviation will be sqrt(36) = 6

from the formula, you get:
z = (15 - 15) / 6 = 0

now, if you are looking at a distribution of means, then that's a different story because the distribution of mean is calculated using the standard error rather than the standard deviation.

the standard error is equal to the standard deviation divided by the square root of the sample size.

if you sample size is 50, then the standard error would be equal to 6 / sqrt(50) which would then equal .849

if the mean of your sample is 15 and the mean of your population is also 15, you will still get a z score of 0 as shown below:

z = (x - m) / se

substituting known values, we get:

z = (15 - 15) / .849 which is also equal to 0.

if you're not dealing with a distribution of sample means then go with the first explanation.

z = (x - m) / sd

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

represents the mean, is the value of the data point, and is the positive square root of the variance.

John

My calculator said it, I believe it, that settles it

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