A precise count of the number of New Jersey students who refused to take the new PARCC exam last month remains an elusive target.

But state now says the “opt-out” rate ranged from 3 percent in the elementary schools to 15 percent among students in their junior year of high school, according to memos sent to school districts yesterday by the Christie administration.

State officials said they wanted to give school officials additional information for when they talk to families about the controversial standardized tests.

And they said they view the percentages as a positive sign, given the intense debate over the testing that has gripped the education establishment for several months.

“Our goal is to have these numbers much smaller,” said state Education Commissioner David Hespe in an interview. “But given the context, and the millions spent on PARCC, and the concerns about its administration, and it being a brand-new test, we were very encouraged by the numbers in especially the youngest grades.”

Hespe blamed the higher opt-out rates in the high schools to some mixed messages -- including from the state itself – about the importance of the tests. The state has delayed making PARCC a graduation requirement.

But he expressed satisfaction that the families of the youngest students had clearly bought in to the PARCC exams.

“They voted with their feet,” Hespe said.

Still, Hespe didn’t downplay the public-relations challenge that has emerged around the controversial testing.

“Clearly we have work to do,” he said.

With 900,000 students statewide, it’s difficult to calculate a total number of opt-outs based on the information the state released yesterday.

And state officials weren’t helping. Hespe stressed that the data remains fluid, preventing such a count, and his staff refused to release more precise numbers to explain how they came up with percentages.

Here are the exact “opt-out” percentages, according to the state:

• 3.8 percent of students in districts that include grades 3-6, in both language arts and math

• 4.6 percent of students in districts that serve grades 3-8

• 7 percent in 9th grade, in both language arts and Algebra I

• 14.5 percent in 11th grade in both language arts and Algebra II

Based on rough math off the total number of students taking the tests in each grade each year, the various estimates that have put the “opt-out” total as high as 50,000 students statewide – including one estimate by the state’s largest teachers union -- don’t appear too far off.