BUS606: Operations and Supply Chain Management

The equation for calculating an average is shown below.

$\bar{x}=\frac{1}{N} \sum_{i=1}^{N} x_{i}=\frac{x_{1}+x_{2}+\cdots+x_{N}}{N}$                     (13.3.1)

where

• $\bar{x}$ is the average
  
• $x_{i}$ is the measurement for trial $i$
• $N$ is the number of measurements

This equation relates to Six Sigma because it is the value that you aim for when you are creating your product. After millions of products made, you will have a very good idea of what your exact average product specification is. The average is combined with the specification limits, which are the limits that determine if your product is in or out of spec. The wider the specification limits are, the more room for deviation from the average there is for your product. A product specification would be written like this:

$10 \pm 2 \mathrm{~mm}$                                                         (13.3.2)

Where the first number (10) represents the average and the second number (2) represents the amount of error allowable from the average without violating 4.5 standard deviations (on a long term scale). Thus, your product can range from 8 to 12 mm for this example.

The average is a good representation of the a set of data. However, the main problem it experiences is the how it is strongly influenced by outlier values. For example, say a town had a population of 50 people with an average income of $30,000 per person. Now say that a person moves into the town with an income of $1,000,000. This would move the average up to approximately $50,000 per person. However, this is not a good representation of the average income of the town. Hence, outlier values must be taken into account when analyzing data. In contrast to the mean, sometimes the median can be a good representation of a set of data. The median is defined as the middle value of a set of data are arranged in order. The median is immune to outlier values as it basically one value and is not calculated it any way so it cannot be influenced by a wide range of numbers. Both the mean and median can be taken into account when analyzing a set of data points.