The number of known infections with the new coronavirus has grown rapidly in the U.S., with more than 270,000 cases as of Friday. More than 7,000 have died. But there are all kinds of holes in those numbers.

People who got sick—or died—before testing was widely available don’t show up in the tallies. Even now, many people who want to get tested can’t, and some who could get tested choose not to. Some people are tested more than once. That undercount is problematic because it slows policy makers and hampers the public from...