The IDC research group’s latest data says Apple had 8.8% of the US computer market in the second quarter of 2010. But the Gartner research group has the number at 9.8%.

Gartner says Apple shipped 1.79 million Macs during the quarter, compared to 14 million in the second quarter of 2009. In the year-ago period, Apple had, per Gartner, 9.1% of the computer market, so has seen annual growth of 24.7%.

Gartner, like IDC, lists Apple as fourth among US computer vendors. Ahead of it, by market share, are HP (25.7%), Dell (23.7%) and Acer (11.3%).

Worldwide computer shipments reached 82.9 million units in the second quarter of 2010, a 20.7% increase from the second quarter of 2009, according to preliminary results by Gartner. These second quarter results were slightly above the research group’s earlier market outlook. Gartner had expected second quarter computer shipments to grow 19.3%.

“The preliminary second quarter results indicate ongoing improvement of the PC market, and it marks the third consecutive quarter of double-digit growth on a year-over-year basis,” saus Mikako Kitagawa, principal analyst at Gartner. “End-user spending grew approximately 13 percent in the second quarter. Average selling prices (ASPs) continue to decline, but at a much slower rate compared with the last two years.”

Mini-notebook shipment growth slowed significantly in the second quarter of 2010, she adds. Mini-notebook shipment growth still exceeded growth rates of the overall mobile computer market, but mini-notebook growth slowed to the low 20% range compared with more than 70% in the last two quarters.