We use the Yohkoh soft X-ray telescope (SXT) full-disk images made from 1993 to 2000 to manually identify X-ray bright points (XBPs). We also employ the National Solar Observatory (Kitt Peak) full-disk longitudinal magnetograms made between 1992 April and 2001 April and an automatic procedure to identify photospheric bipoles whose magnetic field strength is above 20 G, with a pole size (cross-section) between 5'' and 552, and with pole separation between 55 and 483. We use these data to study statistical properties of XBPs and photospheric bipoles during the declining phase of solar cycle 22 and the rising phase of cycle 23. The XBP number follows well-known anti-cycle variation. The average number of XBPs (~10 per disk image) remained approximately the same from 1993 to 1994. Beginning in 1995 it grew, reached a maximum around 1996 December (~50 XBPs per image), and then dropped back to pre-1995 levels in 1998. By contrast, the average number of photospheric bipoles remained approximately the same (~250 per disk image) between 1992 and 2001, despite sunspot activity changes from high (1992, cycle 22) to low (1996, solar minimum) and a return to high activity again in 2000 (solar maximum, cycle 23). Since we expect that a fraction of photospheric bipoles associated with X-ray bright points is independent of solar activity, we see this as a clear indication that the anti-cycle variation of XBP numbers is not real. Most likely, the variation in XBP numbers is the result of a change in the background brightness of the quiet-Sun corona, which is affected by the presence of active regions. On the other hand, annual latitudinal histograms of XBPs show an excess of coronal bright points at active region latitudes, contrary to the effect of changing background brightness. Photospheric bipoles show no enhancement of their distribution at active latitudes. We consider two alternative explanations for this inconsistency.