2.5: Z-Scores Flashcards
Z-Score
A measure of how far from the mean a data point is in units of standard deviations rather than in units of the original variable.
Z-Score Formula
(Interest Value – Mean) / Standard Deviation
What are z-scores helpful for?
Comparing across measures of different units of measurement.
How is z-score expressed?
As a standardized score; indicating where it lies on the standard normal curve.
How are z-scores referred to?
In terms of standard deviations from the mean
- initial units ignored
How much of the data is in 1 standard deviation?
68%
How much of the data is in 2 standard deviations?
95%
How much of the data is in 3 standard deviations?
99.7%
Standard Normal Curve
A theoretical normal distribution with a mean of 0 and a standard deviation of 1.
What does a standard normal curve have?
One set of parameters for a normal distribution
Can any normal distribution be standardized to a standard normal distribution?
Yes as long as you can create a mean of 0 and standard deviation of 1
What does a standard curve give access to?
Information about proportion under the curve.
What are two characteristics of standard curves?
- Perfectly symmetrical
- Area under the curve is 100% of data
What can z-scores help identify?
Outliers
When is IQR more useful than the standard deviation?
When there is a skewed distribution
- SD is affected by extreme values
