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Chapter 5

Chapter 5.docx

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Kristie Dukewich

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Understanding Statistics Chapter 5  Normal Curve  A theoretical distribution of population scores  A bell-shaped curve that is described by this equation:  Equation of a normal curve: ( )  Y= √  Y= frequency of the given value of X*  X= any score in the distribution  μ= mean of the distribution  σ= standard deviation of the distribution  N= total frequency of the distribution  ∏= a constant of 3.1416  e= a constant of 2.7183  This makes a bell-shaped curve  At the bell curve, there are 2 inflection points where the curves go from being convex downward to convex upward, and are at 1 standard deviation from the mean (μ+1σ and μ-1σ)  Theoretically, it never reaches the horizontal axis, and therefore is asymptotic to it  Area under the Normal Curve  The area between the inflection points accounts for 50% of the area  Between the mean and 1 standard deviation point = 34.13% st nd  Between the 1 and 2 standard deviation points = 13.59  Standard Scores, or “Z-Scores”  To make a raw score meaningful, you need to find the percentile rank  Remember, the percentile rank is the percentage of scores that are below the given score)  If the score is above the μ, then add 50% to account for the half of the scores below the mean, and find the percentage between the mean and the standard deviation  In the example in the book, the mean is 100 for an IQ test and you score 132, which is exactly 2 standard deviations from the mean. So, remember the percentages named above:  Mean  1σ = 34.13  1σ2σ = 13.59  Add these = 47.72%  Now remember to add the 50% from the other side of the bell curve, and you end up with 97.72%  This means that you are smarter than 97.72% of the population set!!  We had to find out how many standard deviations the raw score was from the mean, and in turn we found out the standard score, or ‘z-score’  Equation:
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