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Median

The median is the point at which there are the same number of values above it as there are below it. This can apply to a sample, a full population, or distribution curve.

When the data consists of a finite set (rather than a distribution curve), if there is an even number of data points, the median is the average of the two middle points.

Example 1:

For the following data set…

34,35,35,37,39,40,41

…there are seven numbers. The 4th number, 37, has the same quantity of numbers above it as below it, and is the median.

Example 2:

For the following data set…

34,35,35,37,39,40,41,43

…there are eight numbers. Averaging the 4th term (37) and the 5th term (39), givea the value of 38, which has the same quantity of numbers above it as below it, and is the median.

If you have trouble remembering what the median is, think of the median strip on a highway. It is that area in the middle of the highway that separates the two sides.

In a perfectly normal distribution (bell curve), the median, mode (most common value), and mean (average) are all at the same location.

In a skewed distribution, the mean, median, and mode will have different values. The degree of skewness will dictate how far apart they lie.

What this means is that when looking at a data set you have to make sure you understand what is important to you. Imagine that you have 10 people in a room and want to look at both the median and the mean net worth. The two values may be fairly similar for most groups. But what if two of those people were Bill Gates and Warren Buffett? The average would be in the billions, but the median, meaning the salary separating the bottom five from the top five might be in the $50,000 – $60,000 range. With a few outliers, the difference between mean and median can be pronounced.

Using the Median in Continuous Improvement

While the median is important in many statistical tools, it is used only infrequently by frontline teams in continuous improvement. There simply isn’t a lot of utility in knowing the mid-point of cycle times for a process or what size hole has an equal number of larger ones and smaller ones.

It is generally more practical to know how often a cycle time exceeds a takt time or what percent of holes are outside of a specification limit.

That said, it is still important to know what the median is, and what it means. There will be occasions where you will look at data, possibly in research or when considering a piece of equipment, and will come across a mention of the median. You may also, on even more infrequent occasions, need to do more detailed statistical analysis during a project. The median will likely come up then as well.

 

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