Productivity outside the farming sector rose at an annual rate of 3.6 percent in the first quarter of this year, the Labor Department reported yesterday. In the private sector as a whole, output per person jumped by 3.9 percent, the fastest rise since the end of 1977, the department said.

Both figures were an improvement on the fourth quarter of 1980 when productivity in the nonfarm sector fell by 0.4 percent and dropped by 1.2 percent in the total private sector, again as measured at an annual rate.

The first-quarter improvement reflected an upturn in production that far outpaced increased working hours. However, because of sluggish productivity performance during much of last year, the level of output per person in the business sector was only 1 percent higher between January and March than it had been a year earlier.

In a separate report, the Labor Department yesterday reported that major wage settlements reached in the first quarter of 1981 covered 202,000 workers and provided for pay increases of 9 percent on average in the first year of the settlement and 7.7 percent annually over the life of the contracts. y

About four-fifths of the workers involved were covered by cost-of-living-adjustment (COLA) clauses. The settlements covered fewer workers than in any other quarter since the figures were first collected in 1968, the department said.

The first-quarter contract raises compare with 1980 rises of 9 1/2 percent in the first year and 7.1 percent annually, averaged over the settlement lives. iManufacturing industry settlements were higher in the first quarter than in 1980 but were still lower than the average. This was partly because of the prevalence of COLA agreements.

The Reagan administration says that its economic program of tax and spending cuts will increase work, saving and investment and thus raise productivity growth, which has been disappointingly slow in recent years.

Productivity growth tends to speed up automatically with an economic upturn as companies increase their output before taking on new workers. In manufacturing industry the big spurt in output per person came in the last four months of 1980.

Productivity in that quarter rose by 11.4 percent in manufacturing, as output went up by 24 percent, and hours worked increased by only 11.2 percent. In the first three months of this year manufacturing productivity rose at an annual rate of 1.6 percent.