IQ Tests and Standard DeviationDate: 7/28/96 at 9:2:16 From: Anonymous Subject: Number of Standard Deviations On standard IQ tests, the mean is 100, with a standard deviation of 15. The results come very close to fitting a normal curve. Suppose an IQ test is given to a very large group of people. Find the percent of people whose IQ scores fall into the following categories: 1) greater than 115 2) more than 145 Date: 7/31/96 at 14:34:52 From: Doctor Robert Subject: Re: Number of Standard Deviations First, you must convert your scores to z-scores. A z-score is the number of standard deviations that a particular score lies above (positive z) or below (negative z) the mean. For your examples, the z-score for 115 is z = (115-100)/15 = 1. You then go to a z-table which tells you that 84.13 percent of the scores in a normal population lie below z = 1. Therefore, there must be 100-84.13 = 15.87 percent of the population having IQ's above 115. The z-score for 145 is z = (145-100)/15 = 3. From the tables, 99.87 percent of the population lie below z = 3. Therefore, .13 percent of the population have IQs greater than 145. A z-table can be found in the back of almost any statistics book. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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