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

2. 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.

3. Step 1. First, find the mean of the data set. 5 + 6 + 8 + 9 = 28 5 + 6 + 8 + 9 = 28 28 divided by 4 = 7 28 divided by 4 = 7

4. 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.

5. Step 3. Find the mean of the squared deviation. 4 + 1 + 1 + 4 = 10 10 divided by 4 = 2.5

6. 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.