High-range score distribution

© 2005-2007 Paul Cooijmans

Mixed-item and one-sided tests combined - 2005

Below a histogram of the 916 IQ scores so far on Analogies #1, Association and Analogies (French), Cooijmans Intelligence Test, Final Test, Long Test For Genius, Nemesis, Numbers, QMC #4, Short TFG, Space, Time and Hyperspace, Test To End All Tests, Bonsai, Shock and Awe and Dutch LTFG. These are those of my tests that have good enough norms to be used for this type of aggregation. Each * repesents one score.

As one sees, the winner is... IQ 137. The median score is 141.5.

The typical shape of the distribution has remained stable over the years; a clear mode (137), a steep slope on the low side and a gradual slope on the high side. Remarkable is the gap between 155 and 162, with a pit at 159. From 162 on it picks up the slope again. Truly rare are scores above 168.

This shape is made by two powers: one is self-selection, the other is the actual distribution of intelligence in the world. They meet at 137 for a reason. Why there? My best guess is because 137 lies halfway the world average (about IQ 90) and the world highest IQ (mid-180s; the "tie" at IQ 181 below implies there is at least one score above that waiting to be observed).

In the past I thought the highest IQ was higher, like 194-195, given an average of 100 and SD of 15, following a normal distribution with 6 billion people. But since learning the world average is not 100 but around 90 (on a scale with a British mean of 100), I have begun to see the expected highest IQ must be adjusted downward by a point or 10.

The meaning of the mode at 137 is as follows: below 137, people find high-range tests too hard or are not interested, so the testees there are only a fraction of those who actually have an IQ below 137. The distribution of high-range scores below 137 does not represent the world intelligence distribution.

From 137 on, it becomes normal for people to take high-range tests, and the high-range distribution there does represent the world intelligence distribution (about the top 1/1000 of it).

The estimation of the world average as IQ 90 is not mine, and is based on the national IQs published by Lynn and Vanhanen. I have computed the raw average of national IQs once at 84.3, but didn't weight them by the countries' population size. I suppose those who arrived at 90 did do that.

100*
101
102
103
104**
105
106
107
108*
109
110***
111***
112
113*****
114**
115**
116*
117*****
118*
119**
120*********
121**********
122****
123**************
124*
125*********
126*********
127****
128**************
129**********************
130****
131*************
132********************************
133*****************************
134***********
135********************************************************
136****
137********************************************************************************
138****************************************
139************************************
140*******
141*******
142************************************************************
143****************************
144****************
145***********************************************
146************
147***************
148****************************
149****************************************
150*****************
151*******
152***************
153*******************************************
154****
155***************************
156********
157*****
158**
159
160*
161*****
162*********************
163****
164*************
165**************
166****
167*********
168**********
169
170
171***
172
173*
174*****
175*
176*
177*
178**
179*
180*
181**

Mixed-item tests only - January 2007

Below a new histogram with only scores on tests containing a mixture of item types, which I regard the best indicator of intelligence, and on which the top scores are somewhat lower, similar to the phenomenon that a decathlete performs less on the individual athletics events than do the specialists (in mental ability this difference is much smaller than in physical ability, but it exists nevertheless).

These are 297 scores on the Test For Genius (Short, Long and Revision 2004) and Cooijmans Intelligence Test (Forms 1 and 2). The median is 142 and the mode 137 again. Still there is the characteristic gap in the high 150s, and the continuation of the slope in the 160s and 170s. I sometimes wonder why there is a gap there. Perhaps a characteristic of this group of testees, perhaps the result of too high norms above the mid-150s, perhaps a real phenomenon, a kind of interference node.

108*
109
110**
111*
112
113
114
115
116
117
118*
119
120**
121
122***
123*****
124
125
126**
127**
128******
129****
130****
131************
132
133***
134*****
135***************
136***
137****************************
138******************
139*********
140**
141******
142*********************
143********
144**
145*********************
146*******
147*********
148***********
149*****
150****
151*
152************
153*****************
154*
155********
156
157
158*
159
160
161***
162****
163**
164*******
165*****
166
167*
168***
169
170
171**
172
173*
174***
175**
176
177
178**