The stock market finished the week in a total rout, continuing the broadest, steepest extended decline that analysis can remember.

A drop of 15.07 in the Dow Jones industrial average yesterday put the week's loss at 31.96 points to close at 806.05.

For the last two weeks, the decline totals 91.04 points, or a retreat of more than 10 percent.

"People are taking out their record books to see if there is anything worse in such a short period of time, and it's hard to find anything," said Newton Zinder, vice president for market research at E.F. Hutton. "To have two weeks back to back like this is probably unprecedented."

While the decline in the 30 Dow industrials has been demoralizing, they have outperformed the rest of the market which has seen about 10 times as many stocks dropping as advancing. Yesterday, on a turnover of 39.4 million shares, only 175 issues gained on the New York Stock Exchange while 1,480 stocks declined.

The market has been dogged with worries over the plunging dollar, higher inflation and surging interest rates for the last two weeks.

But analysts are attributing the continued descent in stock prices - with only one advance in the last 10 sessions - to technical factors more than to the sour news background.

The severe damage to the so-called secondary stocks, or companies with smaller capitalizations, is apparently continuing because the customers who bought the shares on debt are getting margin calls from their brokers. And, instead of putting up extra money, are selling out their positions, adding to the downward pressure on prices.

"There's forced liquidation going on here, and there's no indication that it's run its course," said Michael Metz, a vice president in the trading department at Oppenheimer & Co. "The dollar, interest rates and inflation are all taking second place to the internal problems in the market. Every time the market declines, it results in a further deterioration of the equity positions of people who own stock on margin."

Meanwhile, the news background continued to be extremely negative yesterday.

The Labor Department announced that consumer prices rose at a 10 per cent annual rate in September, again piercing the double-digit barrier again.

The dollar, as it has ever since President Carter announced his second stage anti-inflation plan, continued to be under severe pressure in the foreign exchange markets with declines against most major currencies. It hit new lows against the West German mark and Japanese yen.

And Citibank raised its prime rate to 10.25 percent, joining the parade of banks that have increased their base lending rate again this week, as short-term interest rates keep rising.

The market, which was up more than 4 points earlier in the session, closed near its low for the day.

The American Stock Exchange Index was down 5.0 to 141.31 for a single day's loss of 3.5 percent.

And the NASDAQ Industrial Index declined 4.01 points to 121.82 or 3 percent, while the NASDAQ composite index was down 2.75 points to 115.25.