We know that column charts are excellent for presenting information. But what if some of the columns are too tall and hijacking the rest. In a previous article, we discussed few of the approaches. Today let’s learn how to build a cropped chart (broken y-axis chart) using Excel, something like this:
Looks interesting? Read on.
Tutorial to create a cropped chart in Excel
Before we begin: Is this the best chart for this data?
Cropped charts or broken Y-axis charts can be misleading and confusing. That said, in some very rare cases, you may need to use them. My suggestion is simple:
- See if you can use a regular column chart
- See if you can use a regular column chart, crop the tall columns at a certain point and fade them using gradient fills. Then apply labels to them so people know which ones are too tall to show on the chart.
- See if there is any other alternative representation for this data (may be just the numbers in a table?!?)
- If your boss / client / spouse is adamant about broken y-axis chart / cropped chart, then make one.
Step 1: Arrange your data
Let’s say we have the numbers as shown aside.
We will have to set up some extra calculations to make this chart. We need to split each column in to 2 portions.
- Below crop
- Above crop
But we can do this only for columns that are too tall. Also, we need to know 2 things:
- At what point we should crop the value – let’s call this crop
- What is the size of crop – let’s call this size
We also need to print a cropped symbol (2 zigzag or slant lines) at the location of crop, if we crop a column.
First, take a look the the calculation setup.
The formulas for 3 extra columns are:
Remember, our data starts from cell B10.
- Crop: =IF(B10>crop+size,crop,B10)
- Above: =IF(B10>crop+size,B10-crop-size,0)
- Marker: =IF(B10>crop+size,crop,NA())
Step 2: Create a stacked column chart
Select both Crop & Above columns and create a regular stacked column chart. We should get something like this:
Step 3: Add marker series as a line to the chart
Add the marker series (select all the values, copy and paste in to the chart – or use Chart > Select Data > Add option).
Marker series will be added as a stacked column by default.
Right click on it and select change series chart type option.
Change the series to line with markers.
Now, set the line properties to no line so that only markers show up.
At this stage, our cropped chart looks like this:
Step 4: Replace markers with crop symbol
Draw a crop symbol. Here is one I used:
- Draw a box. Fill it with pale white color and remove borders.
- Draw 2 horizontal lines and align them to top & bottom edges respectively.
- Select all three shapes (2 lines and one box) and group them (right click and group).
- Rotate this grouped object a bit.
Copy this object / symbol.
Select the markers on the chart. Press CTRL+V.
Excel replaces the markers with your symbol. (more: use shapes to enhance your charts)
At this stage, our chart looks like this:
Step 5: Format the chart
This is easy. Set both crop & above portions to same color. Adjust gap width between columns if necessary.
Play with both crop and size values until you get the perfect chart.
Step 6: Add labels to your chart
As you have cropped the columns, the axis is no longer relevant. We either need to replace the axis labels with two sets of values (before crop & after crop) or remove the axis & set data labels.
Setting different axis labels requires a bit more tweaking of the chart.
So, let’s go with data label route.
First remove the vertical axis. To set the labels:
- Select the bottom series of the column chart. Right click and choose data labels option.(Click here for a screenshot of this step)
- This adds default labels.
- Select the labels and press CTRL+1 to format them
- From label options pane, select “Value From Cells” as the source for labels. Note: This is available only in Excel 2013 or above. For older versions use XY Labeler add-in by Rob Bevey.
- Select the original data (in B10 cell onwards) as the source.
- Set up label properties (location, font, font size, color as you see fit)
- Done!
That is all. Your cropped chart is ready.
Download cropped chart template
Click here to download cropped chart example workbook. The workbook contains all the calculations, full chart and all intermediate steps so that you can learn more.
Awesome resources on charts
Raise above the rest with these awesome resources on charting:
- 5 Simple rules to make awesome column charts – podcast
- 6 Best charts to show progress against a goal
- Column / bar chart with lower and upper boundary
- Interactive sales chart using Excel
Struggle with charting? Excel School is for you:
If you are mystified by the Excel charts and spend way more time on them, then consider enrolling in our Excel School program. This will help you learn how to create awesome charts, interactive workbooks, complex dashboards in a structured way.
Visit Excel School to know more about this program and enroll.
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