# Activity Standard Deviation, Range of Activity Estimates 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

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## 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.