5: Chapter Normal Curve
September Master subtitle style Click to edit9-11, 2008
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Why should we care?
Distribution of most variables we measure:
Intelligence Achievement Positive Affectivity Personality Variables
Assumption of many inference tests
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The normal curve
Y= frequency of X X= score = mean of the distribution
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Area contained under the curve
IQ
E.g., IQ scores SAT = 100
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132
52 148
68
84
100
116
A z score is a transformed score that designates how many standard deviation units the corresponding score is above or below the mean
Standard Scores z scores
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X z= X X z= s
mean = 0 standard deviation =1 Raw scores do NOT
In which class are you doing better?
Social Psychology
You got an 87! mean= 80 sd =5 You got a 92! mean = 75 = sd 15
Abnormal Psychology
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Determine the z score for each raw score
X X2 2 4 6 36 3 9 1 1 3 9 X=15 X2= Xbar= 59 3 8/12/10 z
( X ) SS = X N
2
2
s=
SS N 1
X X z= s
Finding the percentile rank of any raw score
1. 2. 3.
Draw the normal curve Place the raw score on the x-axis Shade the targeted area under the curve Calculate z Use Normal Curve Table
4. 5.
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Example
1.
What percentage of the population scores under 650 on the verbal portion of the SAT?
SAT = 500 SAT = 100
1.
What percentage of the population scores between 480 and 650?
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Percentile Rank of 650
.5 or 50% ?
Add the two areas
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percentage of the population scores between
? ?
Add the two areas
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percentage of the population scores between
Subtract one area from the other
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