Federated Department Stores, Inc., yesterday reported its best third quarter in history, a 27.5 per cent increase in earnings on a sales gain of 11.4 per cent. The company is the nation's ninth largest retailers.

Federal also reported increases of 14.7 per cent in earnings and 10.4 per cent in sales for the nine-month period.

Third-quarter sales totaled $1.18 billion with earnings of $45.4 million (94 cents a share) compared with year-earlier sales of $1.05 billion and earnings of $35.6 million (74 cents).

Nine-month sales were $3.29 billion compared with $2.89 billion for the same period in 1976. Earnings were $97.6 billion compared with $85.1 million, and per-share earnings were $2.03, up from $1.77.

Record sales and earnings also were reported by May Department Stores Co., parents of the Hecht Co. of Washington and Baltimore and the 17th largest retailer.

Increases of 27 per cent in earnings per share and 9.4 per cent in sales brought results in the quarter ender Oct. 29 to $15.9 million (71 cents a share) in earnings on $548.3 million in sales from a revised $12.3 million (56 cents) on $501 million in sales a year ago.

Nine-month earnings of $35.4 million ($1.56) compared with revised $31.2 million ($1.37) a year earlier as sales increased by 8 per cent from $1.398 billion to $1.511 billion.

Restatement of 1976 data reflects accounting changes put into effect in the current fiscal year.

Dayton Hudson Corp. earnings were $18.4 million ($1.15 a share) for the third quarter ended Oct. 29, or 22 per cent higher than the $15.1 million (95 cents) earned in the same period one year ago. Consolidated revenues climbed 16 per cent to $529.7 million from $458.5 million in the 1976 third quater.

Both earnings and revenue figures this year were records for Dayton, the 19th largest retailer.

For the nine-month period, Dayton Hudson reported revenues of $1.435 billion, 13 per cent higher than the $1.266 billion in the same 1976 period. Earnings were $37.9 million, up 26 per cent from the $30 million earned in the same period last year. Per-share earnings rose from $1.88 to $2.37.

The No. 20 retailer, Allied Stores Corp., also reported record earnings for the third quarter and first nine months ended Oct. 29.

Net sales for the quarter totaled $454.5 million, an increase of 8.1 per cent over the $420.5 million for the same year ago period, while earnings were $12.9 million (66 cents a share) compared with $10.7 million (56 cents).

Net sales for the fiscal nine-month period totaled $1.25 billion and net earnings were $26.2 billion ($1.34) compared with sales of $1.197 billion and earnings of $22 million ($1.21) for the same period last year.