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Middle is the value that represents the center of a variable. In this case, both the median (3.7) and the mode (3.7) are in middle. This list is negatively (left) skewed as the value 1.0 is very low compared to all other values 4.0, 3.7, 3.7 and 3.7, and thus has an effect on average value. We take average value as middle for normally distributed data, however, in this case, data are left skewed, and therefore, appropriate choice for middle is median. The mode value is rarely taken as a middle value.
If, I look at the routine that I do every day at work, the average time it takes to complete it matters most. The reason for this that there is not much variation in time for doing the routine work (it is a habit), therefore, average time represents the middle. However, in some cases when there is a problem, the time take more than usual, in such circumstances, the median is more appropriate because time taken will be right skewed.
For finding the middle of process, I look first whether distribution is normal or not. For normal distribution, the average represents the middle of the process. If distribution is skewed, than the median represents the middle of the process.
The normal distribution is symmetric and bell shaped. The scores in a normal distribution are more concentrated in the middle than in the tails. It is an example of continuous probability distribution. It has two parameters, the mean mu and the standard deviation sigma that is used to specify a distribution completely.
If we look at a process and can use a tool to normalize the data, or convert it to a normal distribution, than we will be able to know the range of the values for the process. By using a normal distribution, we can set an upper and lower limit for the process mean so that anytime the process mean is outside this range (above upper limit or below lower limit), we will know that there is some problem and the process
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