Z-scores

purpose of z-scores

reveals exactly where a data point lies relative to the mean and how many SD away

SD is

avg. distance from the mean

the sign (+ or -) of the z-scores indicate

is the raw score is above or below the mean

the magnitude (big or small #) of z-score shows

how many SD the score is from the mean

Standard distribution is

a set of raw scores transformed into z-scores (common scale)

shape of standardize distribution

remain the same

mean of standardize distribution is

zero

standard deviation os standardize distribution is

one

z-scores are helpful bc

• tell you more info.

• make different unit scores more comparable

• can give any mean or SD to the distribution

formula for raw score → z-score

z = [x-μ]/σ

formula for z-score to raw score

x = μ + z(σ)

formula for transformation (get new data set that has a specific mean and SD)

x’ =(μ new) + z(σ new)

to transform, you need to

find the z-score for that data and then use the transformation formula