Dummy Data – How to use the Random Functions
Using collected or known data is the best when developing Excel models, but from time to time this may not be available when you are developing your model.
This post will look at some options for setting up Dummy Data using Excels Random functions.
Variability
Real data displays a range of variability, but this variability is generally within ranges or distributions of ranges of results.
All fields type can contain variability
ie: Country, State Names and Zip/Postal Codes, Maybe large lists but are fixed
Peoples Names, Maybe a large lists but are fixed by local rules
Ages, generally less than 80, never less than 0
Dates: Rarely before 1990 or 1900 in rare cases
Lists: are fixed
Numbers: generally random or conforming to a fixed distribution or known trend
Numbers: may include integers, decimals, negatives, extremely large numbers or all combinations
In generating random lists you will need to choose if you want random data, random data within constraints or random with a distribution. The choice is really yours and should in part be based on what the data is being used for and how accurately it needs to reflect reality.
Techniques
The techniques described below are all shown with a worked example in the attached Examples File or the Excel 2003 Example
Each example is annotated below like (Example 4.). ie: Refer to Example 4 in the above example files.
Dates
Setting up Random Dates is a simple process using the Date function.
=Randbetween(StartDate,EndDate)
Dates in a Range of Years
=Randbetween(Date(2000,1,1),Date(2011,12,31))
Will give a list of Random dates between 1 Jan 2000 and 31 Dec 2011 (Example 1.)
(Thanx Mike W)
Dates in a Month
=Date(2010, 6, Randbetween(1,30)
Will give a list of Random dates between 1 June 2010 and 30 June 2010 (Example 2.)
Don’t worry that the above formula (Example 1) can actually produce a 31 Feb 2005, the Date function will happily convert that to 3 March 2005 (Example 3.)
Dates within a Date Distribution
=DATE(2011,7,NORMINV(RAND(), 0,60))
Will give a list of Random dates between approximately 1 Jan 2010 and 31 Dec 2010, with a mean of July 1 and standard deviation of 2 Months (60days) (Example 4.)
Where NORMINV(RAND(), 0,60) will return values between -180 and +180, 99.7% of the time
Text Fields
Dependant on how many items in the list you require there are 3 techniques available
Choose
For small lists of less than 6 to 10 items you can use a simple Choose function (Example 5.)
=Choose(Randbetween(1,6),”Item 1″, “Item 2”, “Item 3”, “Item 4”, “Item 5”, “Item 6”)
VLookup
Using VLookup (Example 6.)
=Vlookup(Randbetween(1,List Length), List, 2)
Index
Using Index (Example 7.)
=Index(List, Randbetween(1, Counta(List) ))
Numbers
Small Random List of Numbers
Random from a small list of numbers (Example 8.)
=Choose(Randbetween(1,6), Numb 1, Numb 2, Numb 3, Numb 4, Numb 5, Numb 6 )
Note that the numbers:
- Don’t have to be in any order,
- Can be integers, negatives or contain decimals
- Can be repeated
eg: =Choose(Randbetween(1,6), 18, 21, -19, 36.4, 18, 24)
Random Integers
Return Integers between Start and Finish (Example 9.)
=Randbetween(Start, Finish)
=Randbetween(50, 100)
Will return an Integer between 50 and 100
Random Numbers
=Rand()
Will return a random number between 0 and 1
=Round(Rand()*100, 2)
Will Return Numbers between 0 and 100 with 2 Decimal places (Example 10.)
Random Numbers Based on a Distribution
=Norminv(Rand(), Mean, SD)
Will return a random number between 0 and 1 based on a distribution of Average = Mean and Standard Deviation = SD
=Norminv(Rand(), 50, 17)
Will return a random number between 0 and 100 based on a distribution of Average = 50 and Standard Deviation = 17, (Example 11.)
Random Numbers Fitting a Trend
If your distribution has to match a trend add a Random component to the Trends equation (Example 12.)
Y=mX+c
= rand() * X + rand()*5
= rand() * A2 + rand()*5
True/False
Choose
Use Choose and Randbetween (Example 13.)
=Choose(Randbetween(1,2), True, False)
If
Use If and Rand (Example 14.)
=If(Rand()<0.5, True, False)
Combination Text and Numbers
The above techniques can be combined to make lists of Alpha Numeric Data
Say your business has a fleet of vehicles (TR=Truck, VN=Van, CAR=Car)
=Choose(Randbetween(1,3),”TR”,”VN”,”CAR”) & Text(Randbetween(1,15),”0#”)
Will randomly choose 1 of “TR”,”VN”,”CAR” and add a random number between 1 and 15 to it format with a leading 0, eg: TR05, (Example 15.)
Other Sources of Data
Random Data
There are a number of web sites where Random Data is available.
http://www.fakenamegenerator.com/order.php
http://www.generatedata.com/#generator
http://www.melissadata.com/lookups/
Open Source Data
There are a number of web sites where Open Source Data is available.
http://www.readwriteweb.com/archives/where_to_find_open_data_on_the.php
Function Used:
Rand: Returns a random number between 0 and 1.
Randbetween: Returns a random Integer between lower and upper limits. Pre Excel 2007 Randbetween was only available through installation of the Analysis Toolpak (Thanx Luke).
Norminv: Returns the inverse of the normal cumulative distribution. That is it returns the X value from a Normal Distribution that has a know Mean and Standard Deviation where the a known cumulative percentage is supplied.
Choose: Choose an item from a list of up to 254 items.
Vlookup: Lookup the matching value from a list and return a data item from another column from the same location.
Index: Retrieve an items from a defined location within a range.
Text: Displays a number as Text with a defined format.
Other Uses of Random Functions
Of course the techniques shown here don’t have to be used for setting up Dummy Data.
One area where Random numbers is used is in Monte Carlo Simulation. This has been discussed at Chandoo.org at Data Tables and Monte-Carlo Simulations in Excel a Comprehensive Guide
Techniques
The techniques described above are all shown with a worked example in the attached Examples File or the Examples File 2003 ver
Limitations in Pre Excel 2007 versions
The Excel function, Randbetween, was only introduced in Excel 2007. As such the exaples above will only work in 2007/10.
However a simple alternative is available
Randbetween(Low, High) = Low + Int(Rand()*(High-Low))+1
Randbetween(90, 100) = 90 + Int(Rand()*10)+1
Examples using this approach are shown in the 2003 Version of the Examples files above.
How have you made Dummy Data or used the Random Functions?
How have you made Dummy Data or How have you used it ?
How have you used Random Numbers in your workbooks ?
Let us know in the comments below:
20 Responses to “Simulating Dice throws – the correct way to do it in excel”
You have an interesting point, but the bell curve theory is nonsense. Certainly it is not what you would want, even if it were true.
Alpha Bravo - Although not a distribution curve in the strict sense, is does reflect the actual results of throwing two physical dice.
And reflects the following . .
There is 1 way of throwing a total of 2
There are 2 ways of throwing a total of 3
There are 3 ways of throwing a total of 4
There are 4 ways of throwing a total of 5
There are 5 ways of throwing a total of 6
There are 6 ways of throwing a total of 7
There are 5 ways of throwing a total of 8
There are 4 ways of throwing a total of 9
There are 3 ways of throwing a total of 10
There are 2 ways of throwing a total of 11
There is 1 way of throwing a total of 12
@alpha bravo ... welcome... 🙂
either your comment or your dice is loaded 😉
I am afraid the distribution shown in the right graph is what you get when you throw a pair of dice in real world. As Karl already explained, it is not random behavior you see when you try to combine 2 random events (individual dice throws), but more of order due to how things work.
@Karl, thanks 🙂
When simulating a coin toss, the ROUND function you used is appropriate. However, your die simulation formula should use INT instead of ROUND:
=INT(RAND()*6)+1
Otherwise, the rounding causes half of each number's predictions to be applied to the next higher number. Also, you'd get a count for 7, which isn't possible in a die.
To illustrate, I set up 1200 trials of each formula in a worksheet and counted the results. The image here shows the table and a histogram of results:
http://peltiertech.com/WordPress/wp-content/img200808/RandonDieTrials.png
@Jon: thanks for pointing this out. You are absolutely right. INT() is what I should I have used instead of ROUND() as it reduces the possibility of having either 1 or 6 by almost half that of having other numbers.
this is such a good thing to learn, helps me a lot in my future simulations.
Btw, the actual graphs I have shown were plotted based on randbetween() and not from rand()*6, so they still hold good.
Updating the post to include your comments as it helps everyone to know this.
By the way, the distribution is not a Gaussian distribution, as Karl points out. However, when you add the simulations of many dice together (i.e., ten throws), the overall results will approximate a Gaussian distribution. If my feeble memory serves me, this is the Central Limit Theorem.
@Jon, that is right, you have to nearly throw infinite number of dice and add their face counts to get a perfect bell curve or Gaussian distribution, but as the central limit theorem suggests, our curve should roughly look like a bell curve... 🙂
[...] posts on games & excel that you may enjoy: Simulating Dice throws in Excel Generate and Print Bingo / Housie tickets using this excel Understanding Monopoly Board [...]
[...] Correct way to simulate dice throws in excel [...]
[...] Simulate dice throws in excel [...]
I'm afraid to say that this is a badly stated and ambiguous post, which is likely to cause errors and misunderstanding.
Aside from the initial use of round() instead of int(),.. (you've since corrected), you made several crucial mistakes by not accurately and unambiguously stating the details.
Firstly, you said:
"this little function generates a random fraction between 0 and 1"
Correctly stated this should be:
"this little function generates a random fraction F where 0 <= F < 1".
Secondly, I guess because you were a little fuzzy about the exact range of values returned by rand(), you have then been just as ambiguous in stating:
"I usually write int(rand()*12)+1 if I need a random number between 0 to 12".
(that implies 13 integers, not 12)
Your formula, does not return 13 integers between 0 to 12.
It returns 12 integers between 1 and 12 (inclusive).
-- As rand() returns a random fraction F where 0 <= F < 1, you can obviously can only get integers between 1 and 12 (inclusive) from your formula as stated above, but clearly not zero.
If you had said either:
"I usually write int(rand()*12) if I need a random number between 0 to 11 (inclusive)",
or:
"I usually write int(rand()*12)+1 if I need a random number between 1 to 12 (inclusive)"
then you would have been correct.
Unfortunately, you FAIL! -- repeat 5th grade please!
Your Fifth Grade Maths Teacher
Idk if I'm on the right forum for this or how soon one can reply, but I'm working on a test using Excel and I have a table set up to get all my answers from BUT I need to generate 10,000 answers from this one table. Every time, I try to do this I get 10,000 duplicate answers. I know there has to be some simple command I have left out or not used at all, any help would be extremely helpful! (And I already have the dice figured out lol)
Roll 4Dice with 20Sides (4D20) if the total < 20 add the sum of a rerolled 2D20. What is the average total over 10,000 turns? (Short and sweet)
Like I said when I try to simulate 10,000turns I just get "67" 10,000times -_- help please! 😀
@Justin
This is a good example to use for basic simulation
have a look at the file I have posted at:
https://rapidshare.com/files/1257689536/4_Dice.xlsx
It uses a variable size dice which you set
Has 4 Dice
Throws them 10,000 times
If Total per roll < 20 uses the sum of 2 extra dice Adds up the scores Averages the results You can read more about how it was constructed by reading this post: http://chandoo.org/wp/2010/05/06/data-tables-monte-carlo-simulations-in-excel-a-comprehensive-guide/
Oh derp, i fell for this trap too, thinking i was makeing a good dice roll simulation.. instead of just got an average of everything 😛
Noteably This dice trow simulate page is kinda important, as most roleplay dice games were hard.. i mean, a crit failure or crit hit (rolling double 1's or double 6's) in a a game for example dungeons and dragons, if you dont do the roll each induvidual dice, then theres a higher chance of scoreing a crit hit or a crit failure on attacking..
I've been working on this for awhile. So here's a few issues I've come across and solved.
#1. round() does work, but you add 0.5 as the constant, not 1.
trunc() and int() give you the same distributions as round() when you use the constant 1, so among the three functions they are all equally fair as long as you remember what you're doing when you use one rather than the other. I've proven it with a rough mathematical proof -- I say rough only because I'm not a proper mathematician.
In short, depending on the function (s is the number of sides, and R stands in for RAND() ):
round(f), where f = sR + 0.5
trunc(f), where f = sR + 1
int(f), where f = sR + 1
will all give you the same distribution, meaning that between the three functions they are fair and none favors something more than the others. However...
#2. None of the above gets you around the uneven distribution of possible outcomes of primes not found in the factorization of the base being used (base-10, since we're using decimal; and the prime factorization of 10 is 2 and 5).
With a 10-sided die, where your equation would be
=ROUND(6*RAND()+0.5)
Your distribution of possible values is even across all ten possibilities.
However, if you use the most basic die, a 6-sided die, the distributions favor some rolls over others. Let's assume your random number can only generate down to the thousandths (0.000 ? R ? 0.999). The distribution of possible outcomes of your function are:
1: 167
2: 167
3: 166
4: 167
5: 167
6: 166
So 4 and 6 are always under-represented in the distribution by 1 less than their compatriots. This is true no matter how many decimals you allow, though the distribution gets closer and closer to equal the further towards infinite decimal places you go.
This carries over to all die whose numbers of sides do not factor down to a prime factorization of some exponential values of 2 and 5.
So, then, how can we fix this one, tiny issue in a practical manner that doesn't make our heads hurt or put unnecessary strain on the computer?
Real quick addendum to the above:
Obviously when I put the equation after the example of the 10-sided die, I meant to put a 10*RAND() instead of a 6*RAND(). Oops!
Also, where I have 0.000 ? R ? 0.999, the ?'s are supposed to be less-than-or-equal-to signs but the comments didn't like that. Oh well.
How do you keep adding up the total? I would like to have a cell which keeps adding up the total sum of the two dices, even after a new number is generated in the cells when you refresh or generate new numbers.
So, how do you simulate rolling 12 dice? Do you write int(rand()*6) 12 times?
Is there a simpler way of simulating n dice in Excel?
I've run this code in VBA
Sub generate()
Application.ScreenUpdating = False
Application.Calculation = False
Dim app, i As Long
Set app = Application.WorksheetFunction
For i = 3 To 10002
Cells(i, 3).Value = i - 2
Cells(i, 4).Value = app.RandBetween(2, 12)
Cells(i, 5).Value = app.RandBetween(1, 6) + app.RandBetween(1, 6)
Next
Application.ScreenUpdating = True
Application.Calculation = True
End Sub
But I get the same distribution for both columns 4 and 5
Why ?
@Mohammed
I would expect to get the same distribution as you have effectively used the same function