Sunday, July 26, 2009

Introduction to Statistics - Mean

As I have received several requests to do so, I am going to put up a couple of posts that explain some basic statistical concepts. The first few will be the mean, median, and mode, the three most common measures of central tendency. Several students find these concepts difficult to grasp at first, but you will see that they are really quite simple. This post will explain the mean.

The mean may sound like a bad thing, but the mean is actually just another word for a concept that you have UNDOUBTEDLY used SEVERAL times up to this point... the AVERAGE! That's right, the mean is what you have always known as the average. (In fact, the average is not the most precise word to use to describe this function... mean is the correct name.) It is remarkable how many times this connection is not immediately presented to the students, and so they feel they are struggling with a new concept, and one that is probably not being taught well! I will briefly go over the calculation of the mean, but please leave a comment if you wish to have any additional details about it.

The arithmetic mean is the sum of a group of values, divided by the number of values used to determine that sum. A familiar example would go something like this:

The grades received for a test in a math class, composed of 12 students, were:
65, 98, 92, 43, 76, 64, 69, 72, 75, 85, 96, 90
What is the mean grade received on this test?

To compute the mean of this set of data, first determine the sum of the grades... this is 925.
Next, you determine the number of values, which was stated as 12.
Divide the sum by the number of values to give.... 77.083333
So the mean grade received on this test was 77%.

It's that simple. The sum of the values, divided by the number of values. :) Let me know if you want more. Otherwise, I will now move on to median and mode. See my post here for tips on how to choose which of these measures of central tendency to use.

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