Question: What is the middle? If we have student scores of 4.0, 3.7, 3.7, 3.7, 1.0 the average would be 3.2 while the median and the mode would both be 3.7. Is one of them really in the middle? How dispersed is this list? That is, how much do the scores vary from the middle? Now, look at a routine you do everyday at work. Which matters most, the average time it takes to complete it, the most frequent amount of time? How would you go about finding the middle on the process?
This type of problem is solved by determining the standard deviation. The standard deviation is defined as the square root of the mean of the sum of the squares of the differences between all values and the mean.
In this case the calculation would be as follows:
Standard Deviation = Square Root [ ((4.0-3.2)^2 + (3.7-3.2)^2 + (3.7-3.2)^2 + (3.7-3.2)^2 + (1.0-3.2)^2)/5 ]
The result would be: 1.1 ...
This solution shows the calculation of regular measures of central tendency including the mode, mean and median. The concept of dispersion is discussed. Standard deviation is calculated as a measure of dispersion of the data in this exercise with all mathematical steps detailed.