Associated Topics || Dr. Math Home || Search Dr. Math

### IQ Tests and Standard Deviation

```
Date: 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/
```
Associated Topics:
High School Statistics

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search