1. Measures of Variability
Learning to calculate the
Standard Deviations

2. Measures of Variability
Using the Deviation formula to calculate the Standard Deviation.
These formulas define what a standard deviation is but are cumbersome to calculate from.

3. Measures of Variability

4. Measures of Variability
Using the Deviation formula to calculate the Standard Deviation.
We can also calculate the SD using the deviation formula when we have grouped data.

5. Measures of Variability

6. Measures of Variability
Calculator Formula
The formula you will almost always use to calculate the SD is the calculator formula.

7. Measures of Variability

8. Measures of Variability
Computing the Standard Deviation from Grouped data
Need to correct for error due to grouping.
Sheppard’s correction for grouping
SD not the same, even with symmetrical distributions.
If there are as many as class intervals, the correction really makes little difference.

9. Measures of Variability
Summary of Standard Deviation
S.D. is the most used and most important measure of dispersion. Related to Variance.
Arithmetic operations can be performed with it
Most stable measure of dispersion.
68% of the scores fall ±1 S.D.
95.4% of the scores fall ±2 S.D.
99.74% of the scores fall ±3 S.D.

10. Measures of Variability
Relationships among measures of dispersion

11. Measures of Variability
Next:
Measures of Skewness
Measures of Kurtosis
Standard Scores and other neat stuff