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The average or arithmetic mean (commonly just called the mean) is a measure of the central tendency of a sample. In layman’s terms, this is simply a way of describing what a representative item from a group would look like.
The arithmetic mean is calculated by dividing the sum of the elements in the sample by the number of elements.
The formula is…
Arithmetic mean = element 1 + element 2 + … + element n / n
Most people know how to calculate the mean of a group. What is not as widely understood is what the mean (or average) really indicates.
It is often thought to be the center of a group. In truth, the middle number is called the median. When the data is evenly distributed, the median and mean are close. When there are outliers or an uneven distribution, the data is skewed, separating the mean and median.
Unfortunately, the average alone rarely tells us anything useful. Using the mean to make decisions is that it can be misleading without more information. For example, if you are working in a service center, and have a target of getting products turned around within 5 days, and your average is 3.5, are you doing a good job? Without more information, you would be hard pressed to answer that question. You don’t know what the shape of the distribution is, nor do you know how many orders are over the 5 day target. The same hold true on part dimensions. An average may be in spec, but many individual parts can be out of spec.
Averages can be a good indicator of change, however. Comparing daily averages, for example, can help you see if a process is shifting. Comparing a sample’s average to a historical average can indicate if something unusual is happening in a process.
Averages are also useful for comparisons. For example, you may be interested in seeing which model of a machine in a factory has the highest average productivity when it comes time to buy a new one as demand goes up.
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