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SOC 2205A/B (30)

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Chapter 4

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

by OC505123

This

**preview**shows half of the first page. to view the full**3 pages of the document.**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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