Single-family home sales in the District were down 34 percent in October from the year before, and condominium sales plunged 55 percent over the year, Rufus S. Lusk & Son Inc., a information-gathering firm, reported this week.

The Lusk figures show that 369 houses with a value of $ 13.5 million were sold in October, while 407 valued at $ 25.6 million were sold a year earlier. There were 161 sales of condominiums worth $ 28.8 million, compared with 354 valued at $ 45.9 million the previous October.

Average sales prices in the District also dropped, from $ 112,730 per unit in October 1980 to $ 107,125 in October this year, paralleling a nation-wide trend. Average condominium prices rose over the year, however, from $ 72,305 to $ 83,820.

The average sales prices do not take into account below-market financing discounts that housing economists say have meant real declines in home prices for some time.

Housing Data Reports, which surveys home-building here, found that 88 percent of local builders contacted were offering some kind of financing discounts, with varying degrees of acceptability among buyers. The current "acceptable" interest rate ranges from 12 1/2 percent to 14 1/2 percent, regardless of the plan involved, the newsletter concluded.

It also observed that:

* Financing programs offering FHA or VA loans that the builder has "bought down" two percentage points below market rates "are appealing to the broadest market segment."

* Graduated-rate mortgages, typically starting at 12 7/8 percent and rising a point per year to 15 7/8 percent, are gaining acceptance.

* Balloon mortgages with rates of perhaps 13 7/8 percent and the entire amount due after the first few years appeal to buyers only if they plan to resell soon or if refinancing is guaranteed when the balloon payment is due.

* Adjustable-rate mortgages, by which rates can be adjusted as often as every month, have not been widely accepted.

* Quite a few builders continued to offer fixed-rate, 30-year financing but usually require 20 percent down payments under this method.