Question 2: What would you estimate the standard deviation of VAS stress to be?
We expect about 95% of observations to be within two standard deviations on either side of the mean. Because of the negative skewness, the outlying observations will tend to be at the left end of the distribution. The four standard deviation range might be 30 to 100. hence the standard deviation should be approximately (100 - 30)/4 = 17.5 mm.
In fact, the standard deviation is 19.1 mm. Any answers within 4 mm of the correct one are good.
We could note that the slight bimodality in the distribution makes the standard deviation a bit bigger than the crude estimation produced.
The point of the exercise is to help you to understand what a standard deviation tells us.
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Last updated: 13 October, 2006.