The nation's factories, mines and utilities operated at 80.2 percent of capacity in October, the lowest level since July, the Federal Reserve Board reported yesterday.

Capacity utilization has been declining as activity in the nation's industries has slowed. The utilization rate was 80.4 percent in September and 80.6 percent in August. The peak during the economic recovery was in July and August 1984 when it was 82 percent, slightly above the 81.7 percent average from 1967 to 1984.

Commerce Department chief economist Robert Ortner said that the slack in the nation's plant capacity is one reason for the slowdown in capital spending.

Such a slowdown, "I think, would be an unfortunate development in the economy," Ortner said. "One thing we really need to increase real output is more capital spending. We still need a lot of plant modernization, cost cutting, productivity improvement."

The low utilization rate also helps explain the moderate rate of inflation, Ortner said.

During the beginning of the most recent economic recovery, capacity utilization grew sharply as economic activity increased, raising fears that bottlenecks and shortages would result and rekindle inflation.

One of the major reasons for the slowdown in plant use is that imports have supplied goods ordinarily produced in U.S. factories, economists have said.

The decline in capacity utilization last month was due in large measure to a brief strike at Chrysler Corp., the Fed said.

"The motor vehicles and parts industry had the greatest fall in operating rate, 4.1 percentage points," the Fed said. A separate category for automobiles declined 5.6 points, the Fed said.

Each of the three major categories declined last month. Manufacturing use dropped from 80.3 percent to 80.1 percent. The rate for mining declined from 80.7 percent to 79.6 percent.

The mining rate has fallen 3.1 percentage points in the last four months, principally because of declines in oil and gas extraction as well as coal and metal mining, the Fed said.

The rate for utilities fell from 82.7 percent to 82.4 percent.

Factory use in nondurable manufacturing dropped 0.1 percentage point, although the operating rate for petroleum products increased 0.8 percentage point, the Fed said. Capacity use of industrial materials producers dropped 0.3 percentage point.

Last October, the overall industry operating rate was 81.1 percent, with the manufacturing rate at 81.1 percent, the Fed said.