Distribution of IQ Scores on the Third Revision (1960) of the Stanford-Binet Intelligence Test




    There is a little IQ distribution data available from the norming of the 1937 (second) revision of the Stanford-Binet IQ test. The test was normed using 3,184 Caucasian schoolchildren, giving the following distribution numbers:

S-B IQ
%
S-B#
Gau.
S-B S

Gau S

L-N S S-B Dev. IQ
ln-norm IQ
160-169
0.03
1
0.3
1
0.3
2.
154.5-160.5?
150-156
150-159
0.2
6
3
7
3.3
11
145.5-153.7
143-149.4
140-149
1.1
35
17
42
20
40
136-144.7
136-142.7
130-139
3.1
99
76
141
96
127
   127-135.2
128-135
120-129
8.2
261
254
402
350

356

   118-126
119-127
110-119
18.1
576
484
978
834
834
   108-117
110-118
100-109
23.5
748
758
1,726
1,592
1,592
     98-107
100-109
90-99
23.0
732
  2,458        
80-89
14.5
461
  2,993        
70-79
5.6
178  
3,171
       
60-69
2.0
64   3,235        
50-59
0.4
13   3,248        
40-49
0.2
6   3,254        
30-39
0.03
1   3,255        









   

 






    The first column in the above table shows the Stanford-Binet IQ range listed in Dr. Terman's table of IQs found among the 3,184 children who were tested for the 1937 Revision of the Stanford-Binet IQ test.
    The second column gives the percentages of children falling within each 10-point range of IQs.
    In the third column, I've multiplied the percentages listed in the second column by the number of children (3,184) in the norming sample to estimate the number of children in each of Dr. Terman's 10-points IQ ranges.
    In the fourth column are the number of children that would be expected in each IQ range if IQs were Gaussian-distributed.
    The fifth column shows the running sum of the numbers of children in each S-B IQ range in the third column. The fifth column represents the numbers of children at or above the IQs in the third column (since IQ frequencies  are usually specified in terms of the number of children at or above a given IQ).
    The sixth column presents the same kind of cumulative distribution that would be expected if IQs were Gaussian-distributed.
    The seventh column displays the same kind of cumulative distribution that would be expected if these IQs were ln-normally-distributed.
    The eighth column exhibits deviation-IQ ranges that would fit the Stanford-Binet IQ frequency data  presented in column 5 (S-B ) 
    The ninth column shows the deviation-IQ ranges that would be predicted by a ln-normal distribution.

    The S-B deviation IQs derived from this data lie about midway between the Gaussian-predicted IQs (which are equivalent to the S-B IQs listed in the first column), and the ln-normal IQs cited in the last column, this normative data gives the children a median IQ slightly above 100, and it shows a profile opposite to the distribution generated by the 1921-22 Terman Study, where there were more children at the highest levels of IQ than are predicted by a ln-normal distribution.
    Of course, the numbers are sufficiently small at IQs above 150 that random sampling fluctuations could tilt the results either way. (For example, it would be easy to find two children with ratio IQs above 160 in this size sample.)