fooled by average #3: and 2 simple tools to avoid it

August 21, 2010

previously I posted two examples of the common misleading use of AVERAGE.

now, I will show my favorite tools (well, it’s graph) to avoid you are fooled by somebody’s using average.

In fact these two graphs are my favorite graphs (other than the pareto diagram): run chart and box plot.

Here is an imaginary story on how you can use those two graphs.

Imagine you are a sales manager, and you have 3 sales officers report to you: Ed, Jon, Lisa.  You have targeted them to sell at least $16/week.  You told them will send the best seller to Bvlgari hotel in Bali for a week of vacation with their family.

Now, by the end of the year, each of them coming to you and reported they have achieved the target. Each of them send you the full 52 weeks actual sales result (in a spreadsheet) and as they said, each of them in average has sold $16/week. Who deserve the nights at Bvlgari hotel?

Fortunately you are smarter now; you can’t be fooled by the average anymore. Not you.

First, you make a simple run chart. I.e. a simple graph showing the sales of each person over the 52 weeks.

Looking at run chart, you can see stability and trend. You can see, if you are using average, all of them has the same average at $16 (see the red bold line).

But this run chart tell you that Ed’s performance is very unstable. Lisa has an exceptional early performance, but she is getting worse and worse over time. Jon has show consistent performance and also he is getting better lately.

Next, to compare their result side by side, you make a box plot. This is a simple chart representing the distribution of each person’s performance.

This graph is strengthen your analysis on their performance.

Now you are about to pick up the phone, to tell the great news to the best sales of the year. Bulgari hotel, Bali…not bad at all…

Readers, do you know which one is the best sales based on the above two graphs?

fooled by average #1: “our company pays averagely the same as our competitor”

August 2, 2010

are you familiar with this ” our company pays averagely the same as our competitor?”

Regardless the use of “average” in above sentence is intentional or simply out of misunderstanding, it is wrong to use only it for representing a population or a group of data.

I’ve been amazed that until today, many people is still using just “average” or “mean” as the representation of a set of data. And more people just take it without question. With the widespread use of spreadsheet, we have to be better than that.

“Average” could be misleading, because it does not tell us the distribution of the data or population. I’ll show you why.

Imagine there are two company: Company A and Company B, each has 10 employees (to make it simple).  In below table, I list the salary of each  employee. NOW, you can see that the AVERAGE of employees salary for Company A equals to Company B. But, you know they are NOT the SAME, don’t you?

When the sample is only 10 data points, you can see with your eyes that there are difference. But if the data points are more than 200, you need other tool.

In this case, standard devation can help.

Standard deviation shows the variation of data in one group. For instance, in Company B, there is one employee (maybe the CEO) who has very high salary while there are several employees are paid less than 4; it means, the variance is high–> shown by the higher standard deviation vs. Company A.

Hence, while the average salary is the same, Company B does not pay employees similar to Company B.

In summary, whenever you hear someone tell you that average X equals to average Y, you need to ask “what is the standard deviation?”. You need to see whether the variance is also similar and whether there is an outlier that drag the average up or down.


basic principle: you should know the shape/distribution of data, standard deviation and the average/median for making a simple conclusion of data

simple, not simplistic

July 7, 2010

I am a fan of simple solution, but NOT simplistic one.

Simplistic means oversimplification of a problem (without deep understanding of more data/facts), taking the most “obvious” solution, taking shortcut and the fastest result. For instance, in simplistic solution, if you cannot sleep for more than 2 nites you are taking some sleeping pills to help you. That’s simplistic.

Simple means taking the uncomplicated solution based on understanding of the facts and data. Uncomplicated means you don’t need the 100% accuracy for solving all the issues but focus on critical few over the trivial many; hence, the 80/20 rule. In the case of you cannot sleep, you will try to collect info/facts on why you cannot sleep (may need an experience people/doctor).  Your root causes could be:

a. stress from office workload

b. taking too much nap during the day

c. your husband is snoring*

In simple solution, you need to take care whichever the real problem is. In either case, none of taking any sleeping pill will help. In fact, that solution can bring more harm because not only it hides you from the real root cause but also it will create another problem such as addiction.

This is quite common sense, but the issue is many big issue comes from this simple thing.

I’ll show you in my next post.


if the real cause is because your husband is snoring while sleeping, the solution is not kick him out of the house. That’s simplistic:). The simple solution can be just using a pair of earplug?

picking the best option

June 28, 2010

In 2005, I faced a situation to decide which path (job)  I need to choose.

Stay or move on? To which company? Company A or B?

If you have been in this situation, you know what I mean. It’s tough

Staying means feeling secure, I know people and how things work but not sure whether it’s the best for the future. Moving to Company A, give me just OK (not great) salary no guaranteed job security, but the job type is just perfect for me and family in term of time flexibility. Company B seem to have  people who are  just right for me. The salary was much better but a lot of travelling.

Which one to choose?

Rather than overloading my brain, I used a decision matrix to find the optimum solution. Might not perfect but it gave me a visual tool to think more structured. Below is what my decision matrix.

If you are not familiar with this kind of matrix, here are the steps to make one:

  1. List all of your critical factors in deciding a job, in my case: match my passion, the compensation & benefit, quality time with family, and so on.
  2. Give weight for each of the factor, the more important the factor, the higher the weight. Total weight should be 100.
  3. Score each of the option according to each factor. Might not need to be precise, the most important thing is the comparative scores among the options.
  4. Total score = cumulative of (weight x score for each factor).
  5. The highest score is your optimum option.
  6. Use your heart and common sense, does it feel right?
  7. If yes, take the offer.

notes – for singles out there, you can use this tool  if you have too many options to find the perfect one

working really hard? really?

June 26, 2010

Now, it’ll be obvious that pareto diagram is my favorite tool.

This I did about a year a go.

Most of the times, I thought I have been working really hard. Spending many hours in office, meeting, travelling, doing analysis and writing reports.

But many times, I did not feel right because the impact from my priority projects and activities were not as good as expected.

Hence, for the sake of curiosity (and a bit insanity), I tracked my own time spending for ALL my activities in a week. And this is the result*

Focus & act on what matters you the most is the key for winning. But, this common sense is not common practice. As you see, I spent too much on irrelevant meetings and reading/responding too many emails (anyone with me?)


* Here’s how I made the diagram:

1. I listed my top 3 priority for the week:

First: Project Tristar (not the real name), “the most important project of the century”, according to my boss.

Second: Cost Reduction project: recently the most popular project everywhere in the world, I think.

Third: Coached underperforming team members

2. Tracked the actual time of each project this week. Includes everything such as discussion, writing email, meeting. If the discussion/meeting is related to your project, put into the project allocation. Otherwise, put into irrelevant meeting, or irrelevant email.

3. Put the data into pareto diagram