Page 39 - Quantitative Data Analysis

Quantitative Data Analysis
Simply Explained Using SPSS

Standard Deviation

The deviation is the difference between an individual value and the
mean. The sum of the deviations of any set of numbers around its
mean is zero. Units are the same as the original scale.
Variance is the square of standard deviation.
Sample Variance formula:

̅
∑

̅
∑
√

Steps to calculate variance:

̅
∑

̅
1. Subtract the mean ( ) from every observation; these are
̅
each a deviation score:

̅

2. Square each deviation score from step 1:

̅

3. Add up all squared deviation scores: ∑

4. Divide the sum of squared deviation scores by the
Standard Deviation

5. Divide the sum of squared deviation scores by the
Standard Deviation

The standard deviation is the square root of the variance.
1. The units are the same as the original units.
For example,

The Theory and Applications of Statistical Inferences 23