Date: 05/10/2001 at 10:34:45 From: Rick Wright Subject: Averages Dr. Math - My fourth grader tells me that the average of a set of data is always computed by adding all the numbers together and dividing by the total number. Isn't this a misconception? I need to provide some specific discussion or an activity to correct his thinking. Please help. Thank you.
Date: 05/10/2001 at 13:17:06 From: Doctor Twe Subject: Re: Averages Hi Rick - thanks for writing to Dr. Math. It depends on how strictly you want to define the term "average." Merriam-Webster's OnLine Dictionary at: http://www.m-w.com/ defines "average" as: 1a: a single value (as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values b: MEAN 2a: an estimation of or approximation to an arithmetic mean b: a level (as of intelligence) typical of a group, class, or series <above the average> 3: a ratio expressing the average performance especially of an athletic team or an athlete computed according to the number of opportunities for successful performance - on average or on the average: taking the typical example of the group under consideration <prices have increased on average by five percent> Later, the dictionary goes on to say: "AVERAGE is exactly or approximately the quotient obtained by dividing the sum total of a set of figures by the number of figures (scored an average of 85 on tests)." This is what mathematicians define as the "mean," and it is the most common meaning of the term "average." (Note that this is exactly definition 1b, and definition 2a also refers to the mean.) The mean is one of three common measures of central tendency, the others being the median and the mode. Medians and modes are also sometimes referred to as averages, as supported by the dictionary's definition 1a. (The median is the middle value of the data set when arranged in ascending order, and the mode is the most frequently occurring value(s) in the data set.) There are also "weighted averages," where some values are given more weight (or counted more often) than other values in the data set. However, for a fourth grader, understanding what an average is and how to compute it (in the common usage of the term) is more important than making distinctions among other types of "average" measures. When your student is a little older, he or she will learn more about statistical measures and tools, and will learn about these other "averages." I hope this helps. If you have any more questions, write back. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
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