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In Beta Distribution, (O 4M P)/6 . Why is M multiply with 4 and not any other number?

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Poonam Jain Project Manager| Morgan Stanley Hicksville, Ny, United States
Beta Distribution= (O+4M+P)/6

Here,
p= pessimistic
r= most likely
o= optimistic
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Pench Batta Enterprise Lean Agile DevOps Coach /SAFe Program Consultant (SPC6)| Capgemini, Inc. Bentonville, Ar, United States
Poonam, the following link has complete details with mathematical derivations.

https://www.deepfriedbrainproject.com/2010/07/pert-formula.html
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Sante Delle-Vergini, PhD Senior Project Manager| Infosys Melbourne, Victoria, Australia
Because it's more likely to occur, or be reflective of a realistic measurement, so the weighting is higher. 4 times higher in fact.
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1 reply by Poonam Jain
Oct 30, 2018 5:14 PM
Poonam Jain
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Thanks for your reply but do you know why4 and not 3,5,6 or any other number?
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Poonam Jain Project Manager| Morgan Stanley Hicksville, Ny, United States
Oct 30, 2018 5:10 PM
Replying to Sante Delle-Vergini, PhD
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Because it's more likely to occur, or be reflective of a realistic measurement, so the weighting is higher. 4 times higher in fact.
Thanks for your reply but do you know why4 and not 3,5,6 or any other number?
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Kiron Bondale Retired | Mentor| Retired Welland, Ontario, Canada
Poonam -

Here's a possible answer - my eyes glazed over halfway through it but you might be braver than me: https://www.deepfriedbrainproject.com/2010/07/pert-formula.html

Kiron
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1 reply by Stéphane Parent
Sep 23, 2019 12:13 PM
Stéphane Parent
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You can skip to the very end of the article. The six sigma is the big clue that the weights for O, ML and P should add up to six.
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Sante Delle-Vergini, PhD Senior Project Manager| Infosys Melbourne, Victoria, Australia
I saw this explanation in a search:

"4/6ths approximates 66.7%, which approximates 68%, which approximates the area under a normal distribution within one standard deviation of the mean."

"The reason why you multiply by 4 to get the Mean (and not 5, 6, 7, etc.) is because the number 4 is tied to the shape of the underlying probability curve."

"The cone of uncertainty uses the factor 4 for the beginning phase of the project."
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4 replies by Anish Abraham, Poonam Jain, Rami Kaibni, and VINAYAK KATKAR
Oct 31, 2018 2:40 AM
Rami Kaibni
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Interesting explanation Sante
Oct 31, 2018 9:25 AM
Poonam Jain
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Great Answer! Thank You.
Oct 31, 2018 11:48 AM
Anish Abraham
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Good explanation, Sante !!
Nov 01, 2018 4:55 AM
VINAYAK KATKAR
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Very Intresting .... Great
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Rami Kaibni
Community Champion
Senior Projects Manager | Field & Marten Associates New Westminster, British Columbia, Canada
Oct 30, 2018 6:19 PM
Replying to Sante Delle-Vergini, PhD
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I saw this explanation in a search:

"4/6ths approximates 66.7%, which approximates 68%, which approximates the area under a normal distribution within one standard deviation of the mean."

"The reason why you multiply by 4 to get the Mean (and not 5, 6, 7, etc.) is because the number 4 is tied to the shape of the underlying probability curve."

"The cone of uncertainty uses the factor 4 for the beginning phase of the project."
Interesting explanation Sante
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Sergio Luis Conte Helping to create solutions for everyone| Worldwide based Organizations Buenos Aires, Argentina
A master class from Mr. Sante Vergini. Just to complement you can take a look here: https://stackoverflow.com/questions/222231...oint-estimation
I have the original paper wrote when Polaris project was run too.
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Poonam Jain Project Manager| Morgan Stanley Hicksville, Ny, United States
Oct 30, 2018 6:19 PM
Replying to Sante Delle-Vergini, PhD
...
I saw this explanation in a search:

"4/6ths approximates 66.7%, which approximates 68%, which approximates the area under a normal distribution within one standard deviation of the mean."

"The reason why you multiply by 4 to get the Mean (and not 5, 6, 7, etc.) is because the number 4 is tied to the shape of the underlying probability curve."

"The cone of uncertainty uses the factor 4 for the beginning phase of the project."
Great Answer! Thank You.
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Keith Novak Tukwila, Wa, United States
The beta distribution is essentially a bell curve of typical probability distribution that applies to many things. A distribution can be symmetrical, biased to the high end or low end, have very long "tails" at the ends, a tall skinny bell shape or a broad fat one, etc.

The simple algebraic formula using the high and low estimates at the ends, 4x the "most likely" estimate and dividing by 6 basically approximates the bell curve describing your estimates as 3 rectangles (small ones at the end and big one in the middle) and finds the average area to get a statistical "most likely" which takes into account where you think you'll be along with how much uncertainty you have on both the high and low sides.
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Anish Abraham Privacy Program Manager| University of Washington Auburn, Wa, United States
Oct 30, 2018 6:19 PM
Replying to Sante Delle-Vergini, PhD
...
I saw this explanation in a search:

"4/6ths approximates 66.7%, which approximates 68%, which approximates the area under a normal distribution within one standard deviation of the mean."

"The reason why you multiply by 4 to get the Mean (and not 5, 6, 7, etc.) is because the number 4 is tied to the shape of the underlying probability curve."

"The cone of uncertainty uses the factor 4 for the beginning phase of the project."
Good explanation, Sante !!
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