We already saw the Three-Point Estimating technique., where factors such as risk and estimation uncertainty are factored in.

Lets consider that we are estimating duration with the three-point technique, where P=Pessimistic Estimate; O=Optimistic Estimate; and M=Most Likely estimate.

Expected Activity Duration (EAD) with triangular distribution = (P + O + M)/3

EAD with Beta distribution = (P + O + 4M)/6

**What is Standard Deviation? **

Standard Deviation is measure of how dispersed a group of values are. In Project Management, we can calculate the Standard Deviation (SD) of the estimates.

Formula is Standard Deviation **(SD) = (P – O)/6**

**Range of Activity Estimates **

Based on the the value of Standard deviation (SD), we can calculate the upper and lower limit values of Expected Activity Duration/Cost. **Range is the difference of Upper and lower limits**

Formula for Range of Expected Activity Duration= **(EAD – SD , EAD+SD)**

Formula for Range of Expected Activity Cost = **(EAC – SD , EAC+SD) **

It is important to remember that, while calculating EAD or EAC here, **we use Beta distribution only** and not triangular distribution.

Another important thing is, Greater the range, greater is risk. i.e.. as Standard Deviation (SD) increases Risk increases.

## Standard Deviation Example, Range of Activity Estimates Example

**Example : **The Pessimistic Optimistic and most likely duration estimates are 10, 40, 30. Calculate the standard deviation and range of the duration estimates.

Sol: Here P=10, O=40, and M=30

Standard Deviation SD = (P – O)/6 = (10-40)/6 = 5

Expected Activity Duration (EAD) =(P+O+4M)/6 = (10+40+4*30)/6 = 170/6 = 28.33

Range = (EAD-SD , EAD+SD) = (28.33-5 , 28.33+5) = (23.33 , 33.33)

**Summary**

- SD measures how dispersed the individual activity estimates are.
- Formula of Standard Deviation (SD) = (P – O)/6
- Range shows the upper and lower limits of the activity estimates
- Formula for Range = (EAD-SD , EAD+SD); where EAD is the Expected Activity Duration in Beta distribution.
- Greater the Range, greater is the risk; As Standard Deviation (SD) increases, risk increases.