The nation's big retailers added up their November sales yesterday and said they think they are on their way to the best Christmas selling season ever.

The big chains reported their sales are generally running 9 to 15 per cent ahead of last year. J.C. Penney Co., Inc., said its November business was up 13.3 per cent, its largest monthly sales increase this year.

The May Department Stores - which includes the Hecht Co. - reported sales were up 9 per cent, which chairman David E. Babcock said "reinforces or our expectations for record-breaking December business."

F.W. Woolworth Co. president Edward F. Gibbons reported a 6.3 per cent gain and said sales the week after Thanksgiving were "outstanding," and indication of "a strong Christmas selling season."

Soft sales during the first half of November were followed by a sharp upturn when the weather turned cold the week before Thanksgiving, several other chairs reported, including K Mart, up 15.9 per cent, and Montgomery Ward, up 7.3 per cent.

In Washington, Woodward and Lothrop, which does not release monthly results, said sales for the third quarter ended Oct. 29 grew from $58.5 million to $60.5 million. Earnings increased to $2.835 million ($1.18 a share) from $2.695 million ($1.12).

Meanwhile, a monthly survey of retail sales in Virginia conducted by the College of William and Mary business school reported a 7.2 per cent sales gain in October.

Professor Leland E. Traywick, who directs the report, said checking account transactions were up by more than 20 per cent as holiday shopping began, boding for a "an excellent Christmas record."

A mid-November surge is consumer confidence that correlates with the pre-Thanksgiving upturn in retail sales was reported by Sindinger and Co., a Pennsylvania marketing consultant. The jump of 11.9 percentage points in the household money supply was the largest ever recorded, the firm said.

Major chain stores reported these sales results:

K mart Corp. $878 million, up 15.9 per cent for the month and $7.65 billion, an 18.5 per cent gain, for the first 43 weeks of the year.

Sears, Roebuck and Co., $1.73 billion. up 14.2 per cent for the month and $15.09 billion, up 15.9 per cent for the year so far.

J.C. Penny, $383 million, up 13.3 per cent. Year-to-date volume was up to $7 to billion, a 9.9 per cent gain.

Montgomery Ward, $425 million, up 7.3 per cent for November and 12.4 per cent ahead for the year to $3.61 billion.

F.W. Woolworth, $453.3 million up 7.3 per cent for November and the same percentage for the year to $4.22 billion.

May Department Stores, $217.4 million, up 9 per cent for the month $1.73 billion for the first 10 months of its fiscal year and 8.2 per cent gain.

Carter Hawley Hale Stores - Neiman Marcus in Washington - $151.8 million, up 12.2 per cent for the month: $1.12 billion, up 8.6 per cent, for the first 10 months of its year.

Zayre Corp., $135 million, up 11 per cent for the month and $984 million for the 43 weeks, a 7.7 per cent gain.

The Outlet Co., of Providence, R.I., which runs Phillipsborn stores in Washington and recently agreed to buy WTOP radio, reported its broadcast and retail properties had sales of $63 million for the third quarter ended Oct. 31, up from $35 million last year. Earnings jumped to 1.9 million (80 cents a share) from $1.2 million (53 cents).

For the first three quarters - not yet including the WTOP results - Outlet's net increased from $2.1 million (90 cents) to $3.2 million ($1.30). Sales went from $98 million to $140 million.