Chicago Public Schools says about three of every four ninth-graders now earns a high school diploma, a sizable increase from last year’s revised graduation rate.

On Monday, CPS released overall district graduation rates for the class of 2016, showing that 73.5 percent of students earn a diploma within five years of starting ninth grade, a measure commonly used in large urban school districts. Coincidentally, the percentage of children who finished high school in 2016 after four years is the same, according to CPS.

About 1,400 more students received a diploma in 2016 than in 2015, CPS said.

Janice Jackson, CPS’ chief education officer, credited improvements at open-enrollment neighborhood schools for the bulk of the growth. And she said increases happened all over the city.

Graduation rates rose at open-enrollment high schools by 4.6 points, from 68.5 percent to 73.1 percent, and at charter schools by 0.8 points, from 77.4 percent to 78.2 percent.

Last year, after officials and the mayor finally admitted problems that inflated the graduation rate, that rate was revised to 69.9 percent. But the district has increased its training for schools as well as audits of numbers of kids enrolled and what happens after they leave a high school.

“Another way we trust these numbers is if you look at the fact that more children are graduating. The percentages are one thing, but I think when you look at the fact that more children left CPS with a high school diploma, that’s a fact that’s hard to dispute,” Jackson said, announcing the statistics on the eve of the new school year.

The public schools system’s rise in students finishing high school correlates with increases in on-track rates among freshmen, CPS said, citing research from the University of Chicago’s Consortium on Chicago School Research that supporting ninth-graders to show up for school and pass all their classes is the single-most important factor in getting them across a graduation stage.

At six high schools, half of the students didn’t graduate. Most of those six schools are neighborhood high schools that have hemorrhaged both students and programs. And they’re among 47 high schools still below the average 73 percent rate.

Though 85 schools saw their rates go up, 35 schools saw them decrease, 21 of which had a decrease of more than 2 percentage points.

African-American boys, overall, still have the lowest graduation rates at 57.4 percent. Asian girls have the highest at 91.6 percent. CPS officials said non-English language learning Hispanic students also accounted for large gains, though figures released didn’t account for them.

None of the so-called “options schools” aimed at saving students at risk of dropping out or who’ve already left traditional high schools were on the list. Officials said kids who do graduate from those schools, which are often operated for profit, are counted at the school where they started as freshmen.

This year, Spry Community Links High School, 2400 S. Marshall Blvd., also joined the list of 14 schools that graduate at least 90 percent of students. That’s significant for the school educating students from mostly low-income Latino families.

Spry keeps its students year-round, so they get a huge amount of attention, and it’s a full-service community school with lots of emotional supports and services, Principal Francisco Borras said.

The families stay committed, he said. “This area is very high poverty, high violence, but they choose to stay here because they know I can guarantee, because of our program, I can graduate them. I can get them into college.”

Twelfth grade is optional because students complete their requirements in three years.

“We’ve built that resilience in our kids. All their friends are outside on vacation and our kids are in the classroom,” he said. “So they’re accelerating through high school, and that’s the reason why we have such high graduation rates.”

And Westinghouse College Prep High School now boasts the second-highest rate in the city, with a 97.6 percent five-year rate, just below elite North Side College Prep’s 97.8 percent.

The East Garfield Park school even bested selective schools that don’t also welcome neighborhood kids who enter career-track programs as Westinghouse does, Principal Patrick McGill said by telephone.

He credits his teachers and staff who work together on grade-level teams to make sure every single student is supported, especially the freshmen, saying that “their work is changing the lives of the students.”

Data is shared weekly, meetings are held monthly, but conversations and help happen every day, he said.

“The thing we do is we don’t leave any students behind,” McGill said. “We know all their strengths and weaknesses, and we know what they need to be, where they need to be.”

As for the students who don’t quite make it through — and he estimates that as fewer than 10 last year — “we actually, literally know why every student doesn’t graduate, and that informs the work we do going forward.”