There is data on IQ by State for the United States from 1965.  Supporting the belief of many, the correlation is indeed negative between IQ and rural population (1990 census), r=-.24 N=47, and is almost significant at p=1/21.  However, if one excludes the States with the highest number of blacks per capita, (basically the Confederacy), the correlation reverses to r=.25 N=36, and isn’t quite as significant at p=1/14 (which is to be expected when you reduce N).  As might be expected, the correlation between IQ and blacks per capita is very and significantly negative, r=-.58, N=47 and p=1/85,844.  The 5 highest IQ States as of 1965 were, in order, Montana, New Hampshire, Connecticut, Idaho, Nevada.  Nevada would have been significantly more rural in 1965 as Las Vegas is among the fastest growing areas of the US, so I suspect 1965 census data would yield a more significant and higher correlation between rural white population and IQ.

The correlations mentioned above are presented in scattergram form.  These are ecological correlations which means the data points are not individuals taking tests but rather all individuals in a State represented as an average.  This means it is conceivable that the correlations are misleading if some sort of unexpected trends are represented, such as an exceptional tendency in predominantly rural States for extremely intelligent people to concentrate in the smaller urban areas of those States, thus raising the averages of those States to an exceptionally high level covering up an exceptionally large number of low intelligence individuals in the rural areas of those States.

0.25 CORRELATION across 36 cases PREDICTING IQ1965 WITH RuralPercapita1990+ExcludingAR0+ExcludingGA0+ExcludingLA0+ExcludingNC0+ExcludingAL0+ExcludingTN0+ExcludingMI0+ExcludingKY0+ExcludingMS0+ExcludingWV0+ExcludingMD0. 
The odds of this being due to chance are at least 1 in 14.

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Dimensions [minH, minV], [maxH, maxV]:
[0.074, 97], [0.68, 1e+02]

-0.24 CORRELATION across 47 cases PREDICTING IQ1965 WITH RuralPercapita1990.  
The odds of this being due to chance are at least 1 in 21.

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Dimensions [minH, minV], [maxH, maxV]:
[0.074, 89], [0.68, 1e+02]

-0.58 CORRELATION across 47 cases PREDICTING IQ1965 WITH BlackPercapita1990.
The odds of this being due to chance are at least 1 in 85844.

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Dimensions [minH, minV], [maxH, maxV]:
[0.003, 89], [0.36, 1e+02]