Dinah YoungProject Manager / Software Asset Manager| Prince William CountySpringfield, Va, United States
I am usually really good with the calculations and such from the PMI tests. But one thing I have never quite understood is standard deviation. What is it, what is it supposed to represent, what is it used for. I see a bell curve and 1-3 Sigmas. But I am just not understanding. Can someone explain it to me in simple terms? Saving Changes...
Bruce WentworthConsultant| Wentworth AnalyticsAllentown, Nj, United States
A standard deviation (calculated from the sample) estimates sigma (the usually unknown attribute of the population from which the sample was drawn). For the bell shaped curve (normal distribution), plus or minus 1 sigma should cover 68%, plus or minus 2 sigmas should cover 95%, and plus or minus 3 sigmas should cover 99.7%.
Does that help/make sense?
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2 replies by Dinah Young and George Lewis
Dec 28, 2017 1:30 PM
Dinah Young
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Not really. That is the definition. I do not understand what it actually is used for and what it represents.
Dec 29, 2017 1:50 AM
George Lewis
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yes, indeed...
Saving Changes...
Dinah YoungProject Manager / Software Asset Manager| Prince William CountySpringfield, Va, United States
Dec 28, 2017 1:26 PM
Replying to Bruce Wentworth
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A standard deviation (calculated from the sample) estimates sigma (the usually unknown attribute of the population from which the sample was drawn). For the bell shaped curve (normal distribution), plus or minus 1 sigma should cover 68%, plus or minus 2 sigmas should cover 95%, and plus or minus 3 sigmas should cover 99.7%.
Does that help/make sense?
Not really. That is the definition. I do not understand what it actually is used for and what it represents. Saving Changes...
Guilherme CalobaProduction Engineer| PETROBRASRio De Janeiro, Rio De Janeiro, Brazil
I agree with Bruce. Generally when we are dealing with uncertainty and expert opinion it is far more easy for the SME to explicit values such as P10, P50 or P90 or Minimum, Average and Maximum. We can then use this data to develop our triangular distributions and run risk analysis in our schedule or whatever analysis we want to do. The concept of a standard deviation is quite abstract for non statistical people to grasp! We should make the work easier. Saving Changes...
Nehal ManekDirector Program Planning| Barnes and Noble Digital EducationEast Meadow, Ny, United States
The standard deviation is a measure of the spread of scores within a set of data. The lesser it is, the more the scores are very close to the average. It is usually used in conjunction with mean to summarize the data. A very good use of standard deviation is to make informed decisions.
For example, if you are told that the average starting salary for someone working at Company Statistix is $70,000, you may think, “Wow! That’s great.” But if the standard deviation for starting salaries at Company Statistix is $20,000, that’s a lot of variation in terms of how much money you can make, so the average starting salary of $70,000 isn’t as informative in the end, is it?
On the other hand, if the standard deviation was only $5,000, you would have a much better idea of what to expect for a starting salary at that company. Which is more appealing? That’s a decision each person has to make; however, it’ll be a much more informed decision once you realize standard deviation matters.
Hope this helps. :)
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1 reply by Dinah Young
Dec 28, 2017 2:03 PM
Dinah Young
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So, going back to Bruce's definition. The mean is $70,000 with a standard deviation of $20,000. The $20,000 would be the 1 sigma deviation and 68% of the company is in this range? The 2 sigma may be another $10,000. And 95% of the company would be in the range of $40,000 to $100,000?
Saving Changes...
Bruce WentworthConsultant| Wentworth AnalyticsAllentown, Nj, United States
The standard deviation is a measure of variability or spread. It may be used to determine if a process, represented by a series of measurements, has changed significantly. Examples could be a stock value over time, or the temperature in a controlled environment. Here is a Wikipedia page covering the general concept - https://en.wikipedia.org/wiki/Statistical_dispersion. Saving Changes...
Dinah YoungProject Manager / Software Asset Manager| Prince William CountySpringfield, Va, United States
Dec 28, 2017 1:48 PM
Replying to Nehal Manek
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The standard deviation is a measure of the spread of scores within a set of data. The lesser it is, the more the scores are very close to the average. It is usually used in conjunction with mean to summarize the data. A very good use of standard deviation is to make informed decisions.
For example, if you are told that the average starting salary for someone working at Company Statistix is $70,000, you may think, “Wow! That’s great.” But if the standard deviation for starting salaries at Company Statistix is $20,000, that’s a lot of variation in terms of how much money you can make, so the average starting salary of $70,000 isn’t as informative in the end, is it?
On the other hand, if the standard deviation was only $5,000, you would have a much better idea of what to expect for a starting salary at that company. Which is more appealing? That’s a decision each person has to make; however, it’ll be a much more informed decision once you realize standard deviation matters.
Hope this helps. :)
So, going back to Bruce's definition. The mean is $70,000 with a standard deviation of $20,000. The $20,000 would be the 1 sigma deviation and 68% of the company is in this range? The 2 sigma may be another $10,000. And 95% of the company would be in the range of $40,000 to $100,000?
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2 replies by Bruce Wentworth and Nehal Manek
Dec 28, 2017 2:15 PM
Nehal Manek
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The calculation of ranges is incorrect. As mentioned by Bruce earlier only if the data set follows normal distribution , which is a bell shaped curve, plus or minus 1 sigma should cover 68% of the numbers in the data set, plus or minus 2 sigmas should cover 95%, and plus or minus 3 sigmas should cover 99.7%. In this case - 1 sigma = 68% of people have salaries between 50,000 to 90,000 2 sigma (2*20,000) = 95% of people have salaries between 30,000 to 110,000 3 sigma (3*20,000) = 99.7% of people have salaries between 10,000 to 130,000 If the data set is significantly skewed or has outliers then analysis based on mean and standard deviation may not be appropriate.
Dec 28, 2017 2:19 PM
Bruce Wentworth
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Yes, assuming a normal underlying distribution, and using another $20,000 for each additional sigma (95% in the range $30,000 to $110,000).
Salaries tend NOT to be a nice symmetric normal bell curve, with more of a large cluster at the low end and a long fat tail at the high end.
Saving Changes...
Nehal ManekDirector Program Planning| Barnes and Noble Digital EducationEast Meadow, Ny, United States
Dec 28, 2017 2:03 PM
Replying to Dinah Young
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So, going back to Bruce's definition. The mean is $70,000 with a standard deviation of $20,000. The $20,000 would be the 1 sigma deviation and 68% of the company is in this range? The 2 sigma may be another $10,000. And 95% of the company would be in the range of $40,000 to $100,000?
The calculation of ranges is incorrect. As mentioned by Bruce earlier only if the data set follows normal distribution , which is a bell shaped curve, plus or minus 1 sigma should cover 68% of the numbers in the data set, plus or minus 2 sigmas should cover 95%, and plus or minus 3 sigmas should cover 99.7%. In this case - 1 sigma = 68% of people have salaries between 50,000 to 90,000 2 sigma (2*20,000) = 95% of people have salaries between 30,000 to 110,000 3 sigma (3*20,000) = 99.7% of people have salaries between 10,000 to 130,000 If the data set is significantly skewed or has outliers then analysis based on mean and standard deviation may not be appropriate. Saving Changes...
Bruce WentworthConsultant| Wentworth AnalyticsAllentown, Nj, United States
Dec 28, 2017 2:03 PM
Replying to Dinah Young
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So, going back to Bruce's definition. The mean is $70,000 with a standard deviation of $20,000. The $20,000 would be the 1 sigma deviation and 68% of the company is in this range? The 2 sigma may be another $10,000. And 95% of the company would be in the range of $40,000 to $100,000?
Yes, assuming a normal underlying distribution, and using another $20,000 for each additional sigma (95% in the range $30,000 to $110,000).
Salaries tend NOT to be a nice symmetric normal bell curve, with more of a large cluster at the low end and a long fat tail at the high end. Saving Changes...
Dinah YoungProject Manager / Software Asset Manager| Prince William CountySpringfield, Va, United States
OK. Now can you help me apply this to Risk. I am reading that probability distribution estimates the potential of a risk event to occur over a pre-described range. What would we be mapping in regards to risk?
I am struggling to get my head around this topic.
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1 reply by Nehal Manek
Dec 28, 2017 5:19 PM
Nehal Manek
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I'll try explaining this with a very simple example :
Key activity when performing quantitative risk assessment, is to quantify uncertainty.
If we were describing the uncertainty present in the number of rainy days in a year, this probability distribution function would map each integer between 0 and 365 to a probability.
Example : You are the PM of a bridge construction project and work cannot be done on rainy days. As a PM you would like to quantify this uncertainty.
Data set collected in the past indicating # of rainy days in a year is following a normal distribution. So, higher the standard deviation the greater the probability of risk-event to occur. Since sigma refers to the +/- value from mean, the greater the range the greater the risk event to occur.
Now, the table mentioned below should make sense : Risk increases as SD increases. Mean = 20 days SD = 2 1 Sigma = 18 to 22 days 2 Sigma = 16 to 24 days 3 Sigma = 14 to 26 days
SD = 3 1 Sigma = 17 to 23 days 2 Sigma = 14 to 26 days 3 Sigma = 11 to 29 days
Hope this helps :)
Saving Changes...
mohan muniswamaiahProgram Manager| America Express, Target, Tata Consultancy Services Ltd.,Mohan AssociatesBangalore, Karnataka, India
Before we understand standard deviation, we have to understand why standard deviation was introduced.
Let's hear a story, 4 piece of chocolate is available to eat, we have 4 people to eat the same.
One person does not eat the chocolate due some reason and other three will eat 4 pieces of chocolate equally..
Now if we take average, then one person should have eaten one chocolate each. But in reality only 3 persons have eaten the chocolate.
Average = total number people / no of chocolates =4/4=1.. will not give a correct solution.
Now to avoid such confusion, Standard Deviation came in to existence.
Now how to find how many people had to chocolate... using standard deviation
A define procedure is available on how to calculate standard deviation, when you calculate using that method, you arrive a number for example 2.98
A graph called bell curve is drawn by use of numbers generated from standard deviation calculation. The graph looks like a bell curve. now the central portion of bell curve is the average ( in crude terms or )standard deviation . the distance which amounts to 2.98 ( example number) with in the center of the graph or bell curve is called standard deviation.
Standard deviation is a number which covers 68% area of bell curve.
In above example, in vague terms we can tell that, 68% of " 4 people group " would have eaten at least one piece of chocolate
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