Standard Deviation A Measure of Variation in a set of Data.

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Presentation transcript:

Standard Deviation A Measure of Variation in a set of Data

How to Manually Calculate Standard Deviation Given the data set {5, 6, 8, 9}, calculate the standard deviation. Given the data set {5, 6, 8, 9}, calculate the standard deviation.

Step 1. First, find the mean of the data set = = divided by 4 = 7 28 divided by 4 = 7

Step 2. Find the difference between each data point and the mean (deviation from the mean) and square each of these differences. 7 – 5 = 2,2 squared = 4 7 – 5 = 2,2 squared = 4 7 – 6 = 1,1 squared = 1 7 – 6 = 1,1 squared = 1 7 – 8 = -1,-1 squared = 1 7 – 8 = -1,-1 squared = 1 7 – 9 = -2,-2 squared = 4 7 – 9 = -2,-2 squared = 4 This is called the squared deviation.

Step 3. Find the mean of the squared deviation = divided by 4 = 2.5

Step 4. Find the square root of the mean of the squares. The square root of 2.5 = 1.58 This is the Standard Deviation for this set of data.