  We use weighted mean and median statistics techniques to combine individual
cosmic microwave background (CMB) anisotropy detections and determine binned,
multipole-space, CMB anisotropy power spectra. The resultant power spectra are
peaked. The derived weighted-mean CMB anisotropy power spectrum is not a good
representation of the individual measurements in a number of multipole-space
bins, if the CMB anisotropy is Gaussian and correlations between individual
measurements are small. This could mean that some observational error bars are
underestimated, possibly as a consequence of undetected systematic effects.
Discarding the most discrepant 5% of the measurements alleviates but does not
completely resolve this problem. The median-statistics power spectrum of this
culled data set is not as constraining as the weighted-mean power spectrum.
Nevertheless it indicates that there is more power at multipoles $\ell \sim
150-250$ than is expected in an open cold dark matter (CDM) model, and it is
more 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 a
second peak in the flat CDM model.
