## Normalization by Standard Deviation

Originally found at “http://www.d.umn.edu/~deoka001/Normalization.html”

**Normalization by Standard Deviation**

We normalize the attribute values by using standard deviation.

For Example:

Consider 5 instances which has attribute A with the following values: {-5, 6, 9, 2, 4}

First we calculate the **mean **as follows:

**Mean** = (-5+6+9+2+4) / 5 = **3.2**

Second, we subtract the mean from all the values and square them:

(-5-3.2)^2 = 67.24

(6-3.2)^2 = 7.84

(9-3.2)^2 = 33.64

(2-3.2)^2 = 1.44

(4-3.2)^2 = 0.64

Then we find the **deviation** as follows:

**Deviation** = sqrt ((67.24 + 7.84 + 33.64 + 1.44 + 0.64) / 5) = **4.71**

Now we normalize the attribute values:

**x => (x – Mean) / Deviation**

-5 => (-5 – 3.2) / 4.71 = -1.74

6 => (6 – 3.2) / 4.71 = 0.59

9 => (9 – 3.2) / 4.71 = 1.23

2 => (2 – 3.2) / 4.71 = -0.25

4 => (4 – 3.2) / 4.71 = 0.17