A calculation error led to a lower-than-expected reading on manufacturing activity that pushed stocks down and befuddled economists before the data was corrected — twice.

The Institute for Supply Management corrected its May index more than two hours after its initial 10 a.m. release, saying that it had applied the wrong seasonal adjustment to the data. The error was first discovered by Kenneth Kim, an economist at Stone & McCarthy Research Associates in Princeton, New Jersey, who couldn’t square the raw data with the ISM final report.

“I knew there was a discrepancy that showed something was not right,” Kim said in an interview. Following a hunch, he applied the April seasonal adjustment to the raw data for May and came up with the number released by ISM.

“It showed that’s where the source of the error was,” Kim said. “Once that linked up, I felt very comfortable that was the error that had occurred.”

The ISM reported at 10 a.m. that its factory index dropped to 53.2 in May, signaling a slower pace of expansion that surprised economists and pushed stocks lower. Later, the ISM issued a correction, saying its gauge of manufacturing activity rose to 56 from April’s 54.9. It then issued a second correction, saying the index was 55.4, the number Kim had predicted.

“There was a software error that applied last month’s seasonal adjustment factor to the new data,” ISM factory survey chairman Bradley Holcomb said in an interview. “Everything is considerably higher” than the initial report suggested.

An index reading of 50 is the dividing line between growth and contraction.

Stone & McCarthy, a privately held research firm founded in 1989, is owned by Raymond Stone and William Kanto.