The Bell Curve:  
       Understanding a "normal" distribution.
 

       WAIT!!!!  This is easy!!!!!


Educators and psychologists use standard scores to compare a person's relative strengths and weaknesses.  Intelligence tests, for example, are based on the formula that the Intelligence Quotient is equal to a person's mental age (i.e. the age at which the person's cognitive skills a permit reasoning and problem solving) divided by the person's chronological age (i.e., how old the person is).  It should be expected that an average 10 year old will be able to do the cognitive tasks at the 10 year old level (as determined by research).  Thus the IQ, or intelligence quotient of that child would be 10 divided by 10 which equals 1.  10/10=1.  This quotient then was multiplied by 100 to give an IQ score.  Thus the average intelligence would be 100.

Suppose a person was 10 years old but could only do the cognitive, or intellectual, tasks of an 8 year old child  What would be that child's IQ.  Right 80.  8/10=.8x100=80.

Suppose the 10 year old could do all the the tasks equivalent to that of a 12 year old child.  Now what would the IQ be?  Yes., 120; i.e., 12/10x100.

In reality, due to numerical properties this formula is not as precise as the original developer, Binet, would have liked.  For that reason intelligence tests are normed and standardized on large populations.  For each person a standard score, or z score, can be calculated.  It can be stated that person's intelligence is 130.  That tells us the abilities demonstrated is above the mean score of 100.  It does not tell us how high that score really is. Intelligence and achievement tests have, in general, a standard deviation of 15. Now, it can be learned that the IQ of 130 is 2 standard deviations above the mean IQ of 100; i.e., significantly above the average IQ.  This is clarified in the figure below. The IQ of 100 corresponds to a z score of 0.  Deviations above the average IQ will be higher than 100 and deviations below will be less that 100.  Significant deviations will be greater than one z score; i.e., + or -1, or 15 points as determined by statistical analysis of data relating to IQ and achievement tests.


 
Recall the laws pertaining to the accommodations for those with disability suggest that documentation must demonstrate a significant negative impairment.  Standard scores give a way of measuring that level of significance. When a standard score is greater than 1 standard deviation below either a group mean or an individual mean it is possible to state that a significant discrepancy exists.

If the IQ of a student were 89 would that represent and IQ within the average range of abilities or one that is significantly discrepant.

Right! It is in the average range since it is not greater than 15 points from a mean IQ scorer of 100!
 

 
 



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