The first occurred in the 1920s, when Prohibition created a criminal underworld trafficking alcohol and powering legendary criminals such as Al Capone. In 1930, the homicide rate peaked at 14.6 murders for every 100,000 residents — about 500 people were killed that year, according to data compiled by Northwestern University.

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The second peak occurred during the crime spike in the 1970s through early 1990s. In 1990, the murder rate was 32.9 for every 100,000 people. In 1992, the peak for the city, 939 people were killed. That period saw peaks in other large U.S. cities, as well: Los Angeles had 1,094 homicides that year. San Diego peaked at 167 in 1991; Houston and Dallas peaked in 1991, too. New York's high was in 1990, with 2,245 people killed. Philadelphia's high was also in 1990, with 503 homicides.

Since then, murder rates in America's largest cities (and America on the whole) have plunged. Violent crime rates — including rates for other offenses such as rape and assault — also have fallen precipitously.

That's the simple rebuttal to Trump. In 2015, the number of murders in Chicago was 493 — a bit over half of the city's peak and fewer than were killed at the tail end of the Capone era. Murder is not "reaching record levels," even in the city that is most commonly used as a shorthand for American crime.

Murder rates in many large American cities increased last year, as The Post has reported. In Chicago, the rate increased 15 percent. So far this year, the number of murders is up relative to 2015.

But Chicago's experience isn't universal. New York registered a 4.5 percent increase in its murder rate between 2014 and 2015. Through the first half of 2016, though, the city had fewer shootings than at any point in decades. Year to date, as of this moment, the number of homicides is unchanged.

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"Crime" doesn't only mean "murder," of course. Violent crime in New York is down 1.8 percent from last year — and down 5 percent year to date from 2014. In the two police precincts that serve the city's Bedford-Stuyvesant neighborhood, an area that's still trying to shake its reputation from its more dangerous days, violent crime is down 10 percent in one and up 2 percent in the other.

An analysis by the Brennan Center for Justice found that the change in crime rates in U.S. cities varied widely. In Los Angeles, the violent crime rate increased 25 percent between 2014 and 2015. In Jacksonville, Fla., the rate of violent crimes fell 9.4 percent between 2014 and 2015. On average, violent crime increased 3 percent, per Brennan's analysis — but the crime rate overall in those cities was down 0.1 percent.

The murder rate was up 13 percent, per the center's analysis, half of which was thanks to increases in the murder rates in Baltimore, Chicago and Washington. The long-term trend in Chicago and Washington, though, has been a decline in the cities' murder rates, neither of which is anywhere near record-setting territory.

As we've noted before, the numbers behind crime rates are little comfort to people who hear about senseless killings in U.S. cities or who worry about the safety of their families. More than half of American blacks, Hispanics and working-class whites are worried that they or their family members might be the victims of violent crime, according to PRRI-Brookings polling data.

That makes appeals to those concerns politically powerful. It means that exaggerating the extent of the problem could be beneficial to a candidate for office willing to do such exaggeration.

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