Lesson Standard Deviation

Standard deviation (S.D) or is the measure of the spread of a series from its mean value. S.D. indicates the differences and variability which a set of number has. S.D. is mathematically the square root of variance which is defined as the mean of the square of the differences between the elements and their mean:



The steps to calculate the standard deviation are:
1. Calculate the mean of the series.
2. Calculate the differences between the elements and the mean: for all elements.
3. Calculate the squares of the differences.
4. Calculate the mean of the squares by adding all the squares and dividing by the number of elements.
5. Calculate the square root of the the mean. This is the standard deviation.

Example: Calculate the standard deviation of the series {1,3,12,5,9}.
Solution: The standard deviation can be calculated as follows:
1. Mean of the series = (1+3+12+5+9)/5 = 30/5 = 6
2. The differences between the individual elements and mean would be: {1-6, 3-6, 12-6, 5-6, 9-6} = {-5,-3,6,-1,3}
3. The squares of the differences would be {25,9,36,1,9}.
4. The mean of the squares would be (25+9+36+1+9)/5 = 80/5 = 16
5. The square root of the mean of squares would be = 4
Thus the standard deviation would be 4.