* ISM services index climbs more than expected
* Bank of Japan to pump more funds into economy
* Dow up 1.7 pct, S&P up 2 pct, Nasdaq up 2.2 pct (Updates to midafternoon, changes byline)
By Leah Schnurr
NEW YORK, Oct 5 (Reuters) - U.S. stocks rallied on Tuesday with the S&P hitting its highest level since mid-May as investors cheered encouraging economic data and new steps by the Bank of Japan to stimulate its lackluster economy.
The combination gave investors reason to be optimistic about an improving business climate and the prospect of further steps by governments to pump new life into the global economy. It also underscored expectations that the Federal Reserve will undertake another round of quantitative easing.
"You've got central banks globally continuing to use the tools at their disposal beyond simple interest rate policy to stimulate more capital velocity in the system," said Craig Peckham, equity trading strategist at Jefferies & Company in New York.
Broad sector gains pushed the S&P 500 through the 1,150 level, which has been the top of the recent trading range. More investors have been focused on technical indicators of late, particularly after September's strong bounce.
"It started off being a round number and now it becomes more significant because it has definitely paused there," said Frank Cappelleri, technical market analyst and trader at Instinet in New York.
"Over the past few months, the market has seemed to respect support and resistance more than before. So when one of those levels are taken out, it seems to hold more significance than it has in the past."
The Dow Jones industrial average gained 183.08 points, or 1.70 percent, to 10,934.35. The Standard & Poor's 500 Index climbed 22.44 points, or 1.97 percent, to 1,159.47. The Nasdaq Composite Index jumped 50.94 points, or 2.17 percent, to 2,395.46.
The Bank of Japan set the positive tone early on after it cut its overnight rate target to virtually zero and pledged to buy 5 trillion yen ($60 billion) worth of assets in a fresh dose of economic stimulus.
Wall Street added to gains after data showed the pace of growth in the U.S. services sector accelerated more quickly than forecast last month, while hiring also picked up.
The likelihood of quantitative easing in the United States pushed the euro to its highest level against the dollar since February and lifted commodity prices. Crude oil jumped 1.6 percent above $82 a barrel, while gold hit a record high at $1,340.20 an ounce.
The materials sector led the S&P 500 higher, gaining 2.7 percent, with mining company Freeport-McMoRan jumping 4.4 percent to $91.05.
Elsewhere, Walgreen Co gained 3.3 percent to $34.21 after the drugstore chain posted an unexpected increase in September same-store sales. (Editing by Kenneth Barry)