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Chapter 6

# L33 Psych 300 Chapter Notes - Chapter 6: Normal Distribution, Central Limit Theorem, Standard Deviation

Department
Psychological & Brain Sci (Psychology)
Course Code
L33 Psych 300
Professor
Nestojko
Chapter
6

This preview shows half of the first page. to view the full 2 pages of the document. Chapter 06: The Normal Curve, Standardization, and z
Scores
The Normal Curve - a specific bell-shaped curve that is unimodal, symmetric, and defined
mathematically
The normal curve describes the distributions of many variables
As the size of a sample approaches the size of the population, the distribution resembles
a normal curve (as long as the population is normally distributed)
Building Blocks of Inferential Statistics:
The characteristics of the normal curve
How to use the normal curve to standardize any variable by using a tool called the z
score
The central limit theorem, which, coupled with a grasp of standardization, allows us to
make comparisons between means
Standardization, z
Scores, and the Normal Curve
Standardization - a way to convert individual scores from different normal distributions
to a shared normal distribution with a known mean, standard deviation, and percentiles
z
Score - the number of standard deviations a particular score is from the mean
Like all statistical symbols, the z
is italicized
If your score is 2 standard deviations above the mean, your z
score is 2.0, if your
score is 1.6 standard deviations below the mean, your z
score is -1.6
If the mean is 70, the standard deviation is 10, and your score is an 80,
score is 1.0
The z
distribution always has a mean of zero (0) and a standard deviation of 1
How do we calculate a z
score?
Determine the distance of a particular persons score (X) from the population
mean (u
) as part of the calculation (X - u
)
Express this distance in terms of standard deviations by dividing by the
population standard deviation, o
Transforming z
Scores into Raw Scores
Multiply the z
score by the population standard deviation (o
)
) to this product to get the raw score
Make sure not to forget the negative sign if your z
score is negative
The z
distribution is a normal distribution of standardized scores (z scores), and the
standard normal distribution is a normal distribution of z scores
Using z
Scores to Make Comparisons:
You can compare how you did on one test with how your friend did on a different