Although the courtroom will hear from 11 black or biracial men and a Hispanic woman about their experiences of being stopped repeatedly by the police, the class-action lawsuit — Floyd v. City of New York — claims to represent “hundreds of thousands if not millions of people” who experienced “suspicionless and race-based stops” by the city’s police officers.

The lead plaintiff, David Floyd, a medical student in the Bronx, was stopped twice, according to the suit. The first time was in April 2007, as he walked on the sidewalk; the following year, he said, he was stopped while standing outside his home, helping a neighbor try to get back inside an apartment after becoming locked out. (Mr. Floyd had retrieved a number of keys from his godmother, who owned the house, and was trying them one by one.) The police approached Mr. Floyd and the neighbor and detained them on suspicion of burglary, ordering Mr. Floyd against a wall and searching his pockets.

The trial’s outcome will be decided by a federal judge, Shira A. Scheindlin, who is currently hearing two related stop-and-frisk lawsuits. One of the suits already resulted in a lengthy hearing held late last year, which included testimony by both police officials and Bronx residents who had been stopped.

But that suit deals with only a small number of stops at private residential buildings in the Bronx, whose landlords had authorized the police to patrol there. In that case, Judge Scheindlin has issued a preliminary ruling that many of the stops at issue were unconstitutional, a ruling that would seem troublesome for the city in the Floyd case.

The third lawsuit, still a long way from trial, concerns stops in public housing projects.

But the Floyd suit, which was filed in 2008, challenges the largest number of stops — several million in recent years — and embodies the stop-and-frisk debate most closely. The trial centers on whether street stops in the city have soared because, as the plaintiffs claim, the Police Department has increasingly ignored constitutional limits on its authority to detain people when they investigate behavior that they deem suspicious.