Despite sluggish sales by the three big family department store chains, American retailers had a better Christmas than anticipated, posting sales gains of between 3 percent and 15 percent.

December sales figures announced yesterday showed most major chains finished the month about 7 percent to 9 percent ahead of the year before.

Stores at the bottom and the top of the price spectrum reported the best gains -- two or three times as much as the traditional middle-market retailers, Sears, Roebuck & Co., Montgomery Ward and J.C. Penney.

Penney's sales were up only 3.4 percent, Sear's up 3.9 percent and Ward's up 4.6 percent for the crucial Christmas selling season.

The biggest discount store chain, K mart Corp. posted an 11.8 percent gain, Zayre Corp. was up 15 percent and F.W. Woolworth -- which does more business at its Woolco discount stores than its five and dimes -- was up 8.1 percent.

Similar strong gains were shown by department stores reporting yesterday. Carter Hawley Hale Stores Inc. was up 12.1 percent, led, it said, by the Neiman-Marcus division.

A 9 percent increase was posted by May Department Stores Co. of St. Louis, which owns Hecht's in Washington, and a 15.2 percent gain was shown by Dayton Hudson Corp. of Minneapolis, which recently opened several jewelry stores in the Washington area.

"It was a decent Christmas season, better than a lot of people had expected," commented Monroe Greenstein, who studies retailing companies for Bear, Stearns Co.

He estimated that prices of the kind of merchandise sold by chain stores, increased about 6 percent in the past year so chains whose sales were up less than that actually lost ground.

Various chains reported that their Christmas best sellers included jewelry -- especially gold -- fancy watches, electronic games, down coats and comforters, clothing and fashion accessories. Sales of big-ticket items such as television sets and major appliances were weak.

Despite its relatively modest gains, Sears easily remained the nation's biggest retailer with sales for the five weeks ended Dec. 29 of $2.74 billion. b

K mart was second with sales of $2.20 billion, and J. C. Penney ranked third with December sales of $1.97 billion.

Other major chains reporting yesterday and their sales for the month were: Montgomery Ward, a subsidiary of Mobil Corp., $803 million; F. W. Woolworth, $1.21 billion; Dayton Hudson, $651.5 million; Zayre, $282.3 million; May Department Stores, $566 million; and Carter Hawley Hale, $464.7 million.