Measures of Central Tendency

Answer 1

In my last post I touched on the concept of Central Tendency (CT); that is the theory that in any data set there may be varying values for each data point but that on the whole there is one central value around which the values congregate. I’m going to address three of the most common measures of central tendency in this post. They are the mean, the median, and the mode. The mean, also known as an average, is the most commonly used measure of central tendency that most people are familiar with. This measure is arrived at by adding the individual observations in the data set and then dividing the sum of those values by the number of observations. In my last post I gave the example of daily stock prices that were $3.00, $4.00, $3.00, $6.00, $4.00, $32.00, $3.00. In this instance the sum of the values is 55. And 55 divided by 7 (the number of observations) is $7.86. Therefore the mean of that data set is $7.86. But as I pointed out in my last post, the extreme value of $32.00 skewed the mean higher than any of the other values in the set. That is one weakness of the mean value – it is very sensitive to extreme values. To alleviate that sensitivity, one might seek a different measure of central tendency. Let’s look at the median next, as it does some of the work of desensitizing the CT measure from extreme values. The median is arrived at by arranging the values in order from lowest to highest and choosing the middle value. If the number of values is even the median is considered to be equal to the mean of the middle two values. In our case we have an odd number of values and the middle value is $4.00. $3.00 $3.00 $3.00 --------- $4.00 --------- $4.00 $6.00 $32.00 Thus we see that the median can act to filter out the bias towards extreme values to which the mean is susceptible by placing those values at either end of the continuum and finding the middle of the road value. The last common measure of central tendency that I want to talk about here is the mode. The mode is nothing more than the most commonly reoccurring observation. In our case there are three instances of the value of $3.00, the most of any other value – making $3.00 the mode.