What is distribution?

Standard deviation is a distribution, or pattern, formed by many individual data values.  For instance, a bell shape curve, which is a normal known as a normal distribution, shows many values near the mean value and fewer values at each end of curve.

{Picture of bell curve}

What is standard deviation and variance?

Standard deviation is used to express a distribution.  Since raw values are meaningless to make a comparison (is there a significant difference between 5,000 and 5,001?), the standard deviation tells us exactly how far we are from the mean value.  The variance is similar to standard deviaiton, except it is the squared value.

How do we measure one standard deviation?

 The mean score is obviously 0 Standard deviations away from the mean. Data one standard deviation below the mean is in the 16th percentile. (-34% from mean) Data one standard deviation above the mean is in the 84th percentile. (+34% from mean) Data two standard deviations above the mean is in the 98th percentile. Data two standard deviations below the mean is in the 2nd percentile.

How do we measure standard deviation?

Measuring Standard deviation is very simple.  If you have Microsoft Excel, you can simply use the "Descriptive Statistics" tool by following the directions here

If you want to determine standard deviation by "brute force," follow these steps: