Measuring Variability for Symmetrical Distributions

Standard Deviation The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)

The Formula The formula is easy: it is the square root of the Variance. What is the Variance?

Variance The average of the squared differences from the Mean.

Why square? To calculate the variance follow these steps: Work out the Mean (the simple average of the numbers)Mean Then for each number: subtract the Mean and square the result (the squared difference). Then work out the average of those squared differences.

Example You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

Find the mean first = / 5 (dogs) = Mean = 394

Next Find the Distance between each dog height and the mean Dog HeightMeanDistance

variance To calculate the Variance, take each difference, square it, and then average the result:

Standard Deviation And the Standard Deviation is just the square root of Variance. Variance: 21,704 Standard Deviation:

Useful? And the good thing about the Standard Deviation is that it is useful. Now we can show which heights are within one Standard Deviation (147mm) of the Mean

Example 1 What is the population standard deviation for the numbers: 75, 83, 96, 100, 121 and 125? Find the Mean: 100 Variance: Standard Deviation

Did you get it right? PopulationMeanDistanceSquared Variance: Standard Deviation: 18.23

What is the standard deviation? Ten friends scored the following marks in their end-of-year math exam: 23%, 37%, 45%, 49%, 56%, 63%, 63%, 70%, 72% and 82% Standard Deviation: 16.9%

Standard Deviation A booklet has 12 pages with the following numbers of words: 271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314 Standard Deviation: 22.6