Interpret each of the numbers. How are they computed?
On July 22, 2010 the closing values of three common indices used by people for the stock market were: the Dow Jones Industrial Average was 10259.63, the NASDAQ was 2227.01, and the S&P 500 was 1086.69.
These three measures of the value of stocks in the stock market are a weighted average
(weighted mean or scaled average) of the values of sets of stocks. They are not the mean (arithmetic average) of their prices. The weighted averages consider factors other than just the price such as stock splits and stock dividends. The factors used in computing the stock averages change when companies are added or removed from the index, a stock splits, or a dividends are paid. For more information on this topic see:
In some of the problems prior to this session, we have worked with two common types of averages that are used for measuring central tendency: mean and median. The above problem is an example of another type of average that is used where the mean and median are not a true reflection of the desired information. Often we consider some data values to be more important than other values. So, we use a weighted average (weighted mean or scaled average) to give greater value to some data over other data. Besides the stock market example given above, another situation were weighed average is used is in grading. Scores on tests are often given more value than scores on homework or quizzes.
In this session, we expand the use of the mean (arithmetic average) to large data sets and introduce weighted averages.
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Date last modified: July 23, 2010.
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By Kris Montis and Timothy Peil
