WASHINGTON — The beleaguered housing industry is sending mixed signals, with sales of new homes surging in April by the biggest amount in 14 years while prices endured a record plunge. Analysts said the price drop could provide evidence of builders’ desperation. They are looking to reduce a glut of unsold homes in the face of the worst slump in sales in more than a decade. The Commerce Department reported Thursday that sales of new single-family homes jumped by 16.2 percent in April to a seasonally adjusted annual rate of 981,000 units. That was the biggest one-month sales gain since a 16.4 percent surge in April 1993. Even with the increase, however, sales are 10.6 percent below the level of a year ago. The median price of a new home — the midway point between the costliest and cheapest — fell to $229,100, a record 11.1 percent below the March level. The price was 10.9 percent below the level of a year ago, the biggest year-over-year price decline since 1970. On Wall Street, the stock market retreated as hopes faded that the Federal Reserve will have to resort to an interest rate cut to stimulate […]