14d (edited) • Notes And Study Materials!
PMGT170
So I'm working through this and got to the section about the PERT formula, which states:
O = Optimistic, everything goes smoothly; example: Maria already has a template. No rewrites needed. Maybe 2 hours.
M = Most likely, normal day, few edits, nothing wild; example: She drafts, gets quick feedback, tweaks it. Maybe 4 hours.
P = Delays and hiccups happen; example: Stakeholder changes direction twice, big rewrites. Maybe 7 hours.
so using the PERT formula Expected = (O + 4M + P) ÷ 6
- Optimistic O = 2 hours
- Most likely M = 4 hours
- Pessimistic P = 7 hours
If we plug in those numbers, it becomes:
Expected = (2 + 4·4 + 7) ÷ 6
This is the part where we go back to middle school math and reuse PEMDAS (also known as GEMS, GEMA, BODMAS & BIDMAS) but to be simple it's our order of operations!
First solve in your bracket or parenthesis, keeping order, so move onto your multiplication first.
4x4 = 16, now you're left with (2+16+7) ÷ 6
Finish off your parenthesis then move on to division, (25) ÷ 6
This is going to give us a rounding decimal, and at the end we'll have roughly E = 4.17 hours as the "most likely" estimate.
*Some information has been requested so I'm going to be adding to this a little bit! *
When working with the PERT formula, as seen above it is written as (O+4M+P) ÷ 6, let's expand a little on that and why we have the 4 & 6 within our forumla!
Within the PERT formula the 4 & 6 are included to create a weighted average, not a regular average. Our "most likely" metric is mulitplied by 4 because PERT assumes the "most likely" outcome should matter more than the extreme outcomes. A normal average of the three estimates would be O+M+P÷3 but this treats the three metrics as *equally important* and for real projects that isn't realistic.
Our most likely estimate is usualyl more representative than the "everything goes perfectly" or "everything goes wrong" scenarios. This is why PERT give the most likely estimate extra weight by counting it four times.
Another way you can look at this is O + M + M + M + M + P and this is going to give us six total pieces! 1 for optimistic, 4 for most likely, and 1 for pessimistic. This is also why the denominator is 6 - it's the total weight.
But why not use a different number instead of 4? The 4 is part of the traditional PERT method, it reflects the idea that optimistic and pessimistic values matter, however the most likely estimate should dominate our calculations. PERT is intentionally biased towards realistic middle estimates, while still considering risk on both sides.
If we changed the formula to (O+2M+P)÷ 4 then the most likely metric would still matter more but not be as strong in our caluclations. Alternatively we can go to a slight extreme in the other direction also, this can be visualized with (O+10M+P)÷ 12. In this scenario our most likely estimate would dominate TOO MUCH, and our optimistic and pessimistic estimates are barely going to factor into the results.
So 4 is the classic compromised built into PERT, giving us a more balanced formula, while 6 is giving all values in the formula a chance to be factored into the final weight of the total.
Now lets break down what our other acronyms above were! These were all mnemonics for our Order of Operations in math. These help you know which part of an equation to solve first.
1) PEMDAS
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Meaning:
Solve math problems in this order:
Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
2) GEMS
G = Grouping symbols
E = Exponents
M = Multiplication
S = Subtraction
Important note:
GEMS is not a full order-of-operations mnemonic by itself because it leaves out division and addition. It’s sometimes used in simplified teaching contexts, but it’s incomplete compared to PEMDAS/BODMAS/BIDMAS.
“Grouping symbols” means:
Anything that groups part of an expression together, such as:
( ) parentheses
[ ] brackets
{ } braces
fraction bars
radical symbols in some contexts
3) GEMA
G = Grouping symbols
E = Exponents
M = Multiplication
A = Addition
Important note:
Like GEMS, GEMA is incomplete as a full order-of-operations rule because it leaves out division and subtraction. It’s usually just a simplified classroom memory tool.
4) BODMAS
B = Brackets
O = Orders
D = Division
M = Multiplication
A = Addition
S = Subtraction
Meaning:
Brackets = parentheses or other grouping symbols
Orders = powers, roots, exponents, indices
So BODMAS means:
Brackets
Orders
Division and Multiplication (left to right)
Addition and Subtraction (left to right)
5) BIDMAS
B = Brackets
I = Indices
D = Division
M = Multiplication
A = Addition
S = Subtraction
Meaning:
Indices means exponents/powers.
So BIDMAS is basically the same as BODMAS, just using Indices instead of Orders.
I would like to add an important note here, even within our orders it may appear as though multiplication comes before division & addition before subtraction, but that's not how it actually works. Technically the correct is is that multiplication and division, as well as addition and subtraction, are all done from left to right within the equation.
So for 20 ÷ 5 x 2 you'd do it left to right, 20 ÷ 5 = 4 now move onto the rest of your equation 4 x 2 = 8 not doing multiplication first, but completing the steps from left to right as the equation based on our order of operations calls for.
To make sure it's not overcomplicated all of these ideas are trying to teach the same basic priniciple:
- Do anything inside the grouping symbols, these are your brackets or parentheses [{()}]
- Then do your exponents/powers
- Then do your multiplication/division from left to right
- Then do your addition/subtraction from left to right
I'm sure most people find this simple and easy, but I know some people struggle with math and this may help even a smidge to see it written out this way. Best of luck on your lessons future CEO's! 🧡
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PMGT170
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