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We use weighted mean and median statistics techniques to combine individualcosmic microwave background (CMB) anisotropy detections and determine binned,multipole-space, CMB anisotropy power spectra. The resultant power spectra arepeaked. The derived weighted-mean CMB anisotropy power spectrum is not a goodrepresentation of the individual measurements in a number of multipole-spacebins, if the CMB anisotropy is Gaussian and correlations between individualmeasurements are small. This could mean that some observational error bars areunderestimated, possibly as a consequence of undetected systematic effects.Discarding the most discrepant 5% of the measurements alleviates but does notcompletely resolve this problem. The median-statistics power spectrum of thisculled data set is not as constraining as the weighted-mean power spectrum.Nevertheless it indicates that there is more power at multipoles $\ell \sim150-250$ than is expected in an open cold dark matter (CDM) model, and it ismore consistent with a flat CDM model. Unlike the weighted-mean power spectrum,the median-statistics power spectrum at $\ell \sim 400-500$ does not exclude asecond peak in the flat CDM model.Comment: 35 pages, 5 figure

Binned Cosmic Microwave Background Anisotropy Power Spectra: Peak Location