# This Isn’t Your Average Average

Fact: Averages can be misinterpreted.

That’s a problem.

But would you believe there’s another issue with them. That is, there’s more than one way to calculate an average!

Yep! In grade school it was simple…

To arrive at the average — one number meant to represent the whole bunch – you simply added together the values of each data point, then divided that total sum by the number of data points you sampled.

But when it comes to calculating stock-market averages, the math becomes more complex.

U.S. stock indices are simply calculations made on a basket of component stocks. The intention is to summarize all of the individual stock prices, making it easier to quote the price of the index, rather than quoting the price of each and every stock.

It’s useful to summarize this data into an average. Although the method used to calculate each stock-market index varies. And that can lead to misleading interpretations.

The Dow Jones Industrial Average (DJIA) and the Nasdaq 100 are two of the most widely quoted U.S. stock-market indices, along with the S&P 500, of course. Yet they’re calculated very differently.

The DJIA is a price-weighted index. That means that Visa (NYSE: V), which has the highest share price of the 30 DJIA stocks, at \$221, will have a relatively larger influence on the index’s average than a low-priced stock, like Cisco Systems (Nasdaq: CSCO), which trades for just \$21 a share.

One criticism of this method of calculation is that the per-share price of a stock is a poor gauge of how important the stock’s value is to the overall index. And it’s easily manipulated.

Visa could decide tomorrow to execute a stock split. That’s when the company arbitrarily cuts the per-share price of its stock in half — in this example, from about \$220 a share to \$110.

Alongside this adjustment, the company would also double the number of shares outstanding. So if an investor held 100 shares of Visa, when it was priced at \$220, they would hold 200 shares of stock (now worth \$110 a share), after the split.

Stocks splits, therefore, have no effect on the investor’s account balance. Either way, their investment in Visa is worth \$22,000, before and after the split.

But the split does change how Visa’s stock price influences the DJIA as a whole. After the split, Visa’s lower per-share price means it will move the index’s average to a lesser degree than it did before the split.

If that seems odd to you… good, it should!

Many people agree that a more representative calculation involves weighting each stock in an index by market capitalization (market cap).

Market cap is simply the per-share price of a stock, multiplied by the total number of shares outstanding. It answers the question: “If I owned every single share of Apple’s stock…. How much total value would I own?”

The Nasdaq 100 index is calculated this way.

Apple Inc. (Nasdaq: AAPL) has the highest market cap of the Nasdaq 100, at \$478 billion. As such, changes in Apple’s share price have a relatively larger effect on the index’s average than changes in low market-cap stocks, like Staples (Nasdaq: SPLS), whose stock is worth just \$7.3 billion, in total.

While neither calculation method is technically “right” or “wrong,” understanding the differences can help investors better interpret changes in the averages.

Here are the Top 10 lists for each index:

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Simply put, the Dow Jones Industrial Average is heavily influenced by changes in high-priced stocks. Alternately, the Nasdaq 100 is heavily influenced by changes in stocks with the largest market caps.

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