Bar chart or Line? Scatter plot or box plot? These are the questions we ask ourselves when we set out to make a chart. In this article let me tell you how to pick a chart type so you can make best charts for every situation.
Why is it important to pick right chart?
Because right charts lead to right decisions. We use charts to tell stories, evaluate alternatives, understand trends or find-out if everything is normal. So, an incorrect charting choice can lead to poor judgment of the messages where as a correct chart can lead to right and faster decisions.
How to pick a chart type:
Chart making process can be divided in to 4 steps
- Find-out what you want to say?
- (Re)arrange the data
- Prepare the chart
- Format the chart
1. What is the purpose of this chart?
This is the first and most important step in chart preparation. You must ask yourself, “what is the purpose of this chart?”. Once we know the clear reason why the chart should exist, we will naturally be able to select the correct chart type for that reason.
But I realize that finding the reason itself can be a bit tedious. So I have listed down 6 common reasons that we often have to make a chart:
- to Compare
- to show the Distribution
- to explain Parts of the Whole
- to tell the Trend over time
- to findout the Deviations
- to understand the Relationship
Let us understand these reasons along with the type of charts that go well with these.
1. To Compare:
What it means? You want to compare one set of value(s) with another.
Examples:
- Performance of Product A vs. Product B in 5 regions
- Interview performance of various candidates
Charts that can be used for this reason:
- Bar Charts,
- Column Charts
- Scatter Plots
- Pie Charts
- Line Charts
- Data Tables
2. To Show the Distribution
What it means? You want to show the distribution of a set of values (to understand the outliers, normal ranges etc.)
Examples:
- Distribution of Call waiting times in a call center
- Distribution of bugs found in 10 week software testing phase
Charts that can be used to show distribution:
- Column Charts
- Scatter Plots
- Line charts
- Box Plots
3. Parts of Whole
What it means? You want to show how various parts comprise the whole
Examples:
- Individual product sales as a percentage of whole revenue
- Browser types of customers visiting our website
Charts that can be used to show Parts of Whole:
- Column Charts
- Bar Charts
- Pie Charts
- Data Table
4. Trend over time
What it means? You want to understand the trend over time of some variable(s).
Examples:
- Customer footfalls on the last 365 days
- Share price of MSFT in the last 100 trading sessions
Charts that can be used to show Trend Over Time:
- Column Charts
- Line Charts
- Data Table
5. Deviations
What it means? You want to see which values deviate from the norm.
Examples:
- Failures (or bugs) in the context of Quality Control
- Sales in Various Stores
Charts that can be used to show Deviations:
- Column Charts
- Bar Charts
- Line Charts
- Data Table
6. Relationship
What it means? You want to establish (or show) relationship between 2 (or more) variables
Examples:
- Relationship between Search Phrases and Product Purchases in your website
- Relationship between in-store sales and holidays
Charts that can be used to show Relationship:
- Scatter Plot
- Line Chart
- Data Table
How to pick a chart type when you have more than one reason for the chart?
Simple, use common sense. If I were you, I would either cut down the messages to one or make 2 charts (each conveying one message). If that is not possible, I would consider using dynamic charts or combination charts.
2. (Re)arranging the Data
Even when we know the message and corresponding chart, sometimes, our data may not support us. We then have to rearrange the data. Using excel formulas, pivot tables, tables and data cleaning tools we can easily massage the data.
Once we have the data in required format, we proceed to step 3.
3. Prepare the chart
Since you have already picked the chart type in Step 1, this is very straight forward. Most of the regular charts are available in MS Excel as default charts. You can insert them with few clicks.
But for some special chart types, you may have to prepare the chart by helper series, formatting etc.
4. Format the chart
While most formatting is done as per individual taste, there are some ground rules that apply on almost all charts. Here they are,
- No non-zero axis scale on bar charts [reasons and discussions]
- Make subtle grid-lines (or remove them) [how to remove grid lines]
- Add labels to important points [labeling techniques]
- Add descriptive, bold titles
- Position axis, scales at the right places (for eg. y-axis to the right on a large time series chart)
- Use simple, easy colors
A final word:
The ideas in this post are meant to be guide lines, not final words in the world of visualization. While these rules can help you make a good chart, a great chart take so much more. Knowledge of your data, Passion for what you do and Genuine focus on your audience’ needs can make your chart truly outstanding. All the best.
References:
Communicating Numbers – White Paper by Stephen Few [PDF]
Resources & Further Help:
- Chart chooser – Juice Analytics
- Data vis 101 – How to choose a chart – Hubspot
- Selecting right char type – KD Nuggets
- Charting Principles
- Charting Tutorials from Peltier Tech
- More articles from Stephen Few
- Charting Wisdom from Jorge Camoes
What is the process you use for Chart Selection?
I would love to know the process you use when selecting a chart type. Please share using comments.
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