The average or arithmetic mean (commonly just called the mean) is one of the most common measures of central tendency of a set of data. In layman’s terms, a measure of central tendency is simply a way of trying to describe the middle value of a set of data.

The arithmetic mean is calculated by dividing the sum of the elements in the sample by the number of elements.

The following formula is used to calculate the arithmetic mean:

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 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.

Be careful about assuming a process is working well when an average is within tolerance. You could have a wide spread that makes a significant number of items in the sample fall outside the acceptable range.
Be careful about using averages with regard to people. Mathematically, approximately half of any team will be below the team’s average in any measure. But people have an aversion to being identified as being below average, and it is demoralizing to them to be identified as such. Focus on the problems that bring the overall average down rather than on individuals.

Changing an average for many specifications can be easy. (The exception is process time.) Simply adjust a setting on a machine and the average diameter changes. But that might not improve a process with a wide spread. It might just push the process over the opposite specification limit. Tightening up the variation is often far harder than just moving an average. (See our article on precision and accuracy for more information.)
People often don’t know that they are below average in something. Imagine having a room full of production workers and asking them to move to one side if they are above average in productivity and the other side if they are below average. Do you think the split will be even? Not likely. The term ‘below average’ strikes an emotional blow to people. Be careful about using it, even if true. Instead, focus on the specific problems that are lowering performance.

Mean (Average)