Example of the Application of Standard Deviation to facilitate a decision
Data was collected for a period of 4 weeks. The time taken to get to work from home was recorded in minutes for a period of 2 weeks using Route A and then repeated for a further 2 weeks using Route B. The data was summarised as below:
Using the Average or “Mean” calculation is can be found that for the 10 days ( 2 weeks ) of data collected for Route A that an average of 20mins is found.
Again using the average of “Mean” calculation of route B also for 10 days ( 2 weeks ) an average of 19mins can be found.
The conclusion may be drawn that Route B is faster on average by 1minute ( or 5% in this case – 1min/20mins. )
However, if we also examine the standard deviation we can begin to understand the variation of each Route.
Using a Spreadsheet we can easily calculate the Standard Deviation ( STD ).
For Route A it is 2.98
For Route B it is 6.00 – a larger number indicating greater variation.
Why is this the case?
Well, Route A recorded a Minimum time of 16mins and a Maximum of 24mins. Both not quite the same average of 20mins but neither the min nor max were very far away from being that average of 20mins.
However, for Route B the Minimum time was 12mins and the Maximum 28mins, times which were quite different than the average of 19mins. In other words, the route demonstrated a much higher level of variability.
Many of the times recorded were quite different than the average of 19mins. A high level of variation suggests a high level of unpredictability.
Therefore for this scenario, the better decision based on the recorded data would be to select Route A as the default route for future travel. Although that route is slightly slower on average ( 20mins – 19mins = 1min slower ) ( 5% slower ) it demonstrated a much higher level of consistency. Standard Deviation allows us not only to examine the Mean ( average ) but also the variation around that average.
Through an improved understanding of the recorded data, we can make safer and more reliable conclusions.
Lean Six Sigma | Standard Deviation - What it is and why is used
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