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Chapter 4

Sociology 2205A/B Chapter Notes - Chapter 4: Normal Distribution, Standard Score, Standard Deviation


Department
Sociology
Course Code
SOC 2205A/B
Professor
William Marshall
Chapter
4

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1. Chapter 4: The Normal Curve
4.1: Introduction
The normal curve is a theoretical model
A type of frequency polygon that is unimodal (one single mode/peak)
Symmetrical and unskewed
The mean, median and mode are all the exact same value
Distances along the horizontal axis of the distribution, when measured in standard
deviations from the mean, always encompass the same proportion of total area under the curve
The distance from any given point to the mean is exactly the same
4.2: Computing Z-Scores
To find a percentage of the total area above, below or between scores must first be
converted into Z Scores
Z-Scores have the same values for their mean (0) and standard deviation (1)
Z-Scores standardize the normal curve
Raw units (IQ, cm, dollars etc.) are converted to z-scores
oThis process is the same as changing miles to km etc.
The formula for converting original scores to z-scores in a sample is
Ex. If xbar = 30 and s = 14.14
Scores (Xi) ZScore
10
20
A zscore of 1.00 indicates that the original score lies one standard deviation above the
mean
A zscore of -1.00 indicates that the original score lies one standard deviation above the
mean
In this case with a score of 10, the z score shows that it is 1.414 standard deviation units
away from the mean
4.3 The Normal Curve Table
Consists of three columns
Z-scores in column (a)
Areas between the Z score and the mean of the curve in column (b)
Portrayed in proportions but can be converted to percentages by multiplying by
100
Areas beyond the beyond the Z score in column C
Z (a) Area Between Mean and Z (b) Area Beyond ©
0.00 0.0000 0.5000
0.01 0.0040 0.4960
0.02 0.0080 0.4920
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