Unexplained trading activity Friday caused the price of Washington's Woodward & Lothrop Inc. stock to jump more than 5 points, finishing at 39 3/4 a share, a 52-week high.

Woodies, whose shares are traded on the over-the-counter market, had been as low as 19 1/4 during the year but had climbed to the mid-30s. Trading that resulted in the climb of 5 1/4 points Friday boosted the stock of the department store chain 18.2 percent for the week, 32.2 percent for the latest four-week period, and 97.5 percent for the year-to-date.

Neither Edwin K. Hoffman, Woodies' chairman, nor other officials of the company could be reached over the weekend for an explanation of the surge in the price of the stock.

However, Woodies, which is the largest department store chain based in this region, has been the subject of considerable speculation about a possible merger.

That speculation heightened in the wake of the recent surprise maneuver by Allied Stores Corp. which soon will result in its acquisition of Washington-based Garfinckel, Brooks Brothers, Miller & Rhoads Inc.

Although Woodies' sales have increased steadily over the past five years, earnings have slipped in the past two.

Nonetheless, Woodies is regarded as one of the strongest regional department store chains in the nation and continues as the leading store of its type in this area, the fourth leading retail market.

In addition to its 15 department stores, Woodies owns prime commercial property, including a site opposite its flagship store in downtown Washington. The company already has announced plans for a major joint-venture development on that site, is occupied by its north annex.