Once you start this topic, given the sociopolitical loadedness of it, you must carry through with it to the end.
African cognitive ability based on international assessments
When it comes to calculating the average African cognitive ability based on international assessment tests, there is disagreement about which method to use when transforming the test scores into IQ equivalents. Rindermann uses direct transformation, Lynn prefers equalization of means and standard deviations, and Wicherts prefers regression .
Using the data that Lynn and Meisenberg (2010) give, I computed the African average cognitive ability based on direct transformation, equalization of the means, and regression (data here).
The following countries have at least 1 data point : Mozambique, Nigeria, Swaziland, South Africa, Botswana, Ghana, Zimbabwe The following assessments were included: TIMSS 1995 (science and math), TIMSS 1997 science and math), TIMSS 2003 (science and math), PIRLS 2006 (reading), IAEP 1990 (math), IAEP 1991 (reading), SISS 1983, SIMS 1981.)
Lynn argues that these scores are inflated as a result of low student attendance rates (e.g., low IQ adolescents didn’t attend as frequently in the past) and as a result of the inclusion of tests which were not based on item response theory. If this is true, we should find lower scores on the more recent tests, as they are based on IRT and as the African school attendance rates have increased. After removing the Second International Science Study (1983) and the Second International Math Study (1981), the only tests included from the ’80s, the average scores decrease ~3 points. The decrease confirms Lynn’s view.
There’s no easy resolution to the issue of which method to use and to the issue of which scores to count. At best, we can estimate that the African cognitive ability based on all assessments is 76 ± 5, and we can note that the average is trending downward, a trend which coincides with increased rates of enrollment and increased accuracy of measurement. Given that the African cognitive ability based on more recent assessments is 73± 6, I would offer 73 as the cognitive ability (as assessed by international tests) and note that this figure takes into account attendance rates and other factors.
African cognitive ability based on IQ tests
When it comes to calculating the average African cognitive ability based on IQ tests, there is disagreement about which inclusion criteria to use and there is disagreement about the meaning of the scores [1-4].
Below, I listed Wicherts’ estimate and Lynn’s estimate (as recalculated by me) in addition to the N-weighted average of every test mentioned in 1-5]
The following countries have at least 1 data point: Congo, Ethiopia, Ghana, Mali, Nigeria, South Africa, Zaire, Kenya, Malawi, Nambia, Sudan, Uganda, Zimbabwe, Madagascar
(Non-Raven’s IQ data here.)
Based on their systematic review of the data and rigorous inclusion criteria, Wicherts et al. calculate an average African IQ of 76.5 . Based on the studies deemed representative by Lynn, I calculated an average African IQ of 71 [1,2]*; the summed data mentioned by Lynn and Wicherts, rejected and not, averaged out to an IQ of 73**. I would offer 73 as the true African cognitive ability based on IQ; while this figure is derived from data which includes numerous unrepresentative samples (e.g., IQ tests given to children with parasite infections; IQ tests given to elite university students), the upward and downward biases tend to cancel out. The close agreement between IQs derived from Raven’s matrices, IQs derived from other IQ tests, and IQ equivalents derived from international assessments, factoring in attendance and age, supports this conclusion.
*Lynn corrects student scores down for representativeness. I uncorrected for that. I also excluded Adult CPM scores (above 18) based on Wicherts’ concern; (Wicherts excludes above 11).
**There is disagreement about a few of the scores; I averaged the difference of the disputed amount.
Taking the international assessments and IQ tests together, the measured African cognitive ability stands at ~73.
The meaning of African IQs
IQ is a measure of general intelligence. It can be a poor measure or a good measure. Wicherts et al.  found the following for Raven’s matrices:
The above indicates that Raven’s matrices are poorer measures of g for Africans than for Westerners. The implications of this for the African IQ are not clear.
The meaning of National G
In a sense, life is an IQ (g/G) test both for individuals and for nations of them. When it comes to the cognitive ability of nations, national IQ (G) differences correlate with patents registered, economic growth, GDP, numbers of scientists, rates of HIV, rates of homicides, total national productivity, etc [6, 7, various]. On many of these measures, sub-Saharan Africans collectively do not fair particularly well and this establishes the validity of national IQ (G) differences and with them the validity of IQ differences. What this means with regards to individual g differences is not completely clear — but the national IQ (G) differences are entirely consistent with an interpretation of aggregated individual g differences and, with them, a hereditarian explanation.
 Lynn and Meisenberg, 2010. The average IQ of sub-Saharan Africans: Comments on Wicherts, Dolan, and van der Maas
 Lynn, 2010. The average IQ of sub-Saharan Africans assessed by the Progressive Matrices: A reply to Wicherts, Dolan, Carlson & van der Maas; Lynn and Meisenberg
 Wicherts, et al., 2010. The dangers of unsystematic selection methods and the representativeness of 46 samples of African test-takers
 Wicherts, et al., 2010. Raven’s test performance of sub-Saharan Africans: Average performance, psychometric properties, and the Flynn Effect
 Wicherts, et al., 2010. A systematic literature review of the average IQ of sub-Saharan Africans
 Brouwers, et al., 2009. Variation in Raven’s Progressive Matrices scores across time and placeSymen A. Brouwers
 Rindermann, et al., 2009. The impact of smart fractions, cognitive ability of politicians and average competence of peoples on social development Between nations.
 Gelande, 2008. IQ, cultural values, and the technological achievement of nations