What is the average amount of risk I can expect for an average stock as compared to investing in a mutual fund?

The extremes to your question can be found by doing a Google search on "Enron". The maximum risk with a stock is you are a shareholder when the company files bankruptcy: you wind up with nothing. That's an extreme, but it is a risk. 

As for average amount of risk for an "average stock", there is no way to quantify an answer to your question  as posted. Each stock and every industry those stocks represent have their own trading characteristics. For example, the "average" technology stock will swing more widely in price over time than will a utility stock. The trade term for this swing parameter is called beta. Beta is an expression of how volatile a stock is when compared to or measured against "the market" overall. Tech stocks are high beta, utility stocks are low beta.

Mutual funds have betas also depending on how their portfolios are constructed. The portfolio of any mutual fund will vary depending on a number of factors including the types of stocks in the portfolio, weighting of the various stocks in the portfolio and the benchmark the fund is being measured against.

Rather than buying "a stock", I'd look at an Exchange Traded Fund (ETF). That will lower your overall market risk and give you diversification to avoid another Enron. If you opt for an Index ETF, be careful which index you chose and the construction of the portfolio. ETF's in general cost less to own than mutual funds and give you more control over what you own. All index funds are NOT created equal.

There is no way to accurately answer your question.

First, I assume you are talking about stock mutual funds. So to begin, a mutual fund by definition will help reduce some concentration risk by investing in many stocks, as opposed to just one stock. This allows the well-performing stocks to offset the poor-performing stocks (in theory).

However, a mutual fund can still take on tremendous amounts of risk, depending on the type (and number) of stocks it invests in. There are funds that invest in just a handful of very risky stocks. On the flip-side, there are index funds that may invest in 500-1000 (or more) stocks, representing entire indexes.

So I guess to give some some sort of direction - a "typical" index fund (such as an S&P 500 index fund) is going to present less risk than investing in one, single stock.

Beyond that, I'm not sure how to direct you, as there are very few individual stocks that would be considered "less risky" than an entire index.