30.812857142857144

16.0

12.75

108.75

43.18

The Standard Deviation is a widely used measurement of variability or diversity of a set of measurements. Volitility in the stock market is the Standard Deviation of the value of a stock. Standard Deviation shows how much variation or "dispersion" there is from the "average" (the mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large range of values. A useful property of Standard Deviation is that, unlike the variance, it is expressed in the same units as the data. Let's use the vertical position of the sliders below as the data values. Move the sliders up and down.

0.18

-1.0

0.18

5.550932997511062

The first step is to find the average of the data samples. The average is the sum of the values divided by the number of values. The sum of the values is

+

+

+

+

+

+

which is

. There are

data values. The average is

. Now that we know the average, we can find out how much each sample differs from the average. Subtract the average from each sample. We need the square of each difference. Add up the squares

+

+

+

+

+

+

and take the average of those to get

. This called the variance. Taking the square root gives a Standard Deviation of

. It is in the same units as the data values. For a normal distribution (or bell curve) of data, 68.2% of the values will be within one standard deviation of the average.

2.0

19.61

6.0

39.0

31.04

7

5.571428571428571

0.0

6.0

10.0