The stock market put the finishing touches on its best week so far in 1978 with another steady advance Friday.

Analysts said traders continued to look ahead hopefully to President Carter's scheduled speech on inflation and other economic issues next Tuesday.

The Dow Jones average of 30 industrials climbed 5.63 to 769.58, extending its gain for the week to 12.22 points. That marked the average's best weekly performance since it picked up 14.55 last Dec. 19-23.

The daily New York Stock Exchange tally showed advances outnumbering declines by about an 8.5 spread. The NYSEs composite index of more than 1,500 common stocks climbed .22 to 50.41.

Brokers noted speculation that the president might call for some significant new policy moves in his speech next week. The president has promised to propose a new plan designed to combat the recent acceleration in the inflation rate.

Otherwise, the news background was mixed. The government reported Friday morning that the unemployment rate rose from 6.1 to 6.2 percent in March, interrupting a steady decline from the 7 percent level that began last September.

On the positive side, the Federal Reserve's weekly report issued late Thursday showed a smaller-than-expected $600 million rise in the basic measure of the money supply.

Brokers said the date tended to relieve some of investors' recent fears of an impending move by the Fed to tighten credit in its efforts to curb inflation.

The day's volume on the Big Board totaled 25.16 million shares, against 27.36 million Thursday.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchange and in the over-the-counter market, totaled 28.75 million shares.

Standard & Poor's index of 400 industrials rose .45 to 99.17 and S&P's 500-stock composite index was up .38 at 90.17.

Indicators for the American Stock Exchange and the over-the-counter market continued to post new highs since 1973.

The Amex market value index, which pushed through the 130 level for the first time on Thursday, climbed another .96 to 131.81. The NASDAW composite index of OTC issues rose .76 to 108.23.

At 4 p.m. J. Ray McDermott was the most active NYSE-listed issued up 3/4 to 26 5/8. A company spokesman said he knew of no reason for the activity in the stock.

Airco was the second most active, soaring 5 5/8 to 49 1/4. BOC International said it planned to take over the company by acquiring Airco's stock at $50 a share as soon as possible.

Marshall Field was the third most active issue, up 4 1/2 to 24. Company officials were not immediately available for comment on the stock. Two Wall Street brokers, however, said there was speculation a move was underway to oust the firm's management which recently fought off a $40-a share takeover bid by Carter Hawley Hale.

Curtiss-Wright fell 3/4 to 20 3/8 and Kennecott Copper added 1/4 to 20. A bitter proxy fight is in progress over Curtis-Wright's efforts to stock control of Kennecott.

Dynalectron was the most active Amex issue, up 1/4 to 5. New York Times A Stock was second, up 1 1/4 to 22 7/8. Total Petroleum was third, off 1/4 to 9 1/8.

Interpol rose 1 3/4 to 37 1/8 in active trading. The company said Thyssen-Bornemisza, an international holding company, intends to proceed with plans to buy Interpol stock at $40 a share.

Resorts International B stock, which climbed 8 1/4 points to 64 Thursday before trading was halted, was suspended from trading for 10 days by the Securities and Exchange Commission.

Resorts has sought a temporary gambling license that would allow it to begin operating its $50 million hotel-casino at Atlantic City, N. J., by Memorial Day. The A stock fell 1 3/4 to 27 5/8 in active trading.