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Hui will share excel tutorials, implementations with us once a week. Please visit About – Hui to learn more about him.
This week I am going to introduce a method for allowing single points to be highlighted and interactively moved in Excel Scatter / X-Y Charts and Line Charts.
You will see a lot of these style charts in various places where you want to highlight various aspects of the chart to your audience. It is a great technique for complex scientific and engineering charts where you may have hundreds or thousands of points.
Introduction
Excel charting basically has 2 styles of charts with these being Y value vs X Value charts and Y value vs X Label charts.
Examples of the X Value charts are Scatter and Bubble charts. Examples of the X Label charts are Line, Column, Surface, Area, Radar and Bar charts.
The basic differences between these is that the former has a variable X Axis and the later has a fixed X-Axis spacing between subsequent data points.
Some members of the X Label charts can display a value-type X axis when the X entries are dates, ie: The X values are plotted proportionally to the dates they represent. These types include Line, Area, Column, and Bar (Thanx Jon)
Y value vs X value (Scatter Charts)
As these charts are plotting Y vs X directly onto the chart, it is simple to add a series which contains the points you want to highlight.
It is worth noting that chart series for Scatter Charts don’t have to have an equal number of entries in each series. We will use this add a new series with just one point.
Method:
Goto Pg1 of the sample file. Sample File
My Data is an X-Y set of data in B2:C41, each Y value in Column C is plotted on the chart against the corresponding X value.
To plot a single point it is a matter of adding a new data series to the chart
The new series will be the 2 cells at B43:C43
1. Setup 2 lookup cells
In B43 put the equation =OFFSET(B$1,$B$44,0)
In C43 put the equation =OFFSET(C$1,$B$44,0)
Note that both these formula retrieve a value that is the value in the Cell Reference cell, B44, below B1 and C1 respectively.
2. Setup a Cell Reference cell
Put a value in B44 for now say 1
3.Add a new Data Series to the Chart
Right click on the chart and goto Select Data
Add a New Series
Series Name Highlight
X Values =’Pg1′!$B$43
Y Values =’Pg1′!$C$43
4. Add a slider
The slider is already installed
5. Set the Sliders Cell Link, Min, Max and other details
You will now have a new data point which will be at point 1 on the chart
6. Format the New Data Series
Right Click the new point and Format Data Series
Select a larger Marker Size and make it a Bold Red to stand out
7. Add a data Label to the series
Right Click the New Series and select Add Data Labels
8. Format the Data Label
Right Click the New Series and select Format Data Labels
On the Labels Options Tab, Tick the X & Y values
Select the Label and change the Font to a Bold and Increase Size so that it stands out
Use:
As you move the slider the Highlighted point will move back and forwards across the screen and show both the location and X & Y Values of the data point.
How Does This Work?
The chart contains a second series consisting of a single point (x,y) which has been formatted to make it stand out on the chart
The coordinates for the new point are retrieved from the My Data list by using an offset from the top of the list.
The offset retrieves its offset value from a Cell Reference cell which in turn is controlled by a slider.
Why use Offset instead of Vlookup or Index/Match?
We aren’t concerned with looking up the actual value of the highlighted point, we are interested in retrieving for example the 9th data point from the list and the the 10th or 8th as we move the slider. The Offset only cares about how far it has to go to get the value, not the value.
By doing this we can mix up the X values, as Scatter charts allow you to do, and offset will happily retrieve data in order and doesn’t care about duplicates or having sorted data. Type any values into the X Column and watch as the offset happily maintains the highlighted point.
Line Charts
As these charts are plotting Y vs the position of the value on the X-Axis, a slightly different method is employed to highlight a point of interest.
For Line Charts we will add a new series to the chart and then use a method for hiding the non-highlighted points so that only the highlighted point is visible.
Method
Goto Pg2 of the sample file. Sample File
1. Setup a Cell Reference cell
Setup a Cell Reference cell by putting a 1 in D43
2. Add a New Data Series
Besides the sample data, add a new series Highlight
D1: Highlight
D2: =IF(ROW()-1=$D$43,C2,NA())
Copy D2 down to D27, Don’t worry about the errors #N/A, you put them there.
3. Add a new Data Series to the Chart
Right click on the chart and goto Select Data
Add a New Series
Series Name – Highlight
Y Series =’Pg2′!$D$2:$D$27
Note there is no X Value as the Y values are plotted in order against the existing X Values
You will now have a new data point which will be at point 1 on the chart
4. Format the new Data Series
Right Click the new point and Format Data Series
Select a Bigger marker size and make it a Bold Red to stand out
5. Add Data Labels
Right Click the New Series and select Add Data Labels
Right Click the New Series and select Format Data Labels
On the Labels Options Tab, Tick the X & Y values
Select the Label and change the Font to a Bold and Increase Size so that it stands out
6. Add a slider
The slider is already installed
7. Set the Sliders Cell Link, Min, Max and other details
Use:
As you move the slider the Highlighted point will move back and forwards across the screen and show both the location and X & Y Values of the data point.
How Does This Work?
The chart contains a second series consisting of a Column of #N/A error messages and a single cell containing teh Y value for the corresponding data point
Excel ignores and doesn’t plot the cells with the error message and so only the highlighted cell is plotted
The coordinates for the new point are retrieved from the My Data list by comparing the current Row to the Cell Reference cells value and if they are the same retrieving the Y value, all others rows have an error message inserted.
The slider is connected to the Cell Reference cell and so when the slider is moved the Cell reference cell updates and the new highlighted cell retries its value.
Quick Tip #1:
You can change the highlight from a standard marker to pretty much anything you like
Insert an Icon on your worksheet, Insert Menu, Insert Icon
Format the icon as you wish, Color, Size and Copy the icon
Select the Chart and select the Highlighted data point and Paste
To apply the picture/icon to all points in a series select the series and paste
Quick Tip #2:
You can add multiple highlights using the same techniques described in this post ie: for showing Min and Max values.
Instead of linking the Cell Reference cell to a slider link it to the Minimum or Maximum value of the data: =Min(Range), =Max(range)
Checkout the example on Pg3 of the Sample File: Sample File
FUNCTIONS USED:
Offset: http://chandoo.org/wp/2008/11/19/vlookup-match-and-offset-explained-in-plain-english-spreadcheats/
Row: =Row() returns the Row number of the Current cell
=Row(M10) returns the Row Number of Cell M10 = 10
NA: = Returns the Error Message #N/A
How do you like to highlight your data? Let us all know in the comments below:
What would you like to see discussed as a How To? Let me 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... 🙂
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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