The picture and some fun facts
Take a pause here and give yourself a moment to think about what’s going on in this picture.
Done? Ok, you had a chance for an unbiased opinion.
I saw this image on LinkedIn last week and was much amused. Part of me understands it is a memorable way to highlight the importance of attitude at work. The other part could not help to make fun of this. Translating words to a percentage of importance at work is plain nonsense. Some words even map to more than 100%, e.g.
nonsense translates to
105. Still, it’s easy to ridicule things, but there’s little value to it, so I decided to investigate a bit further.
What are the odds?
words is a standard file on all Unix-like OS, found in
/usr/share/dict/words. It contains a newline-delimited list of 235886 dictionary words. I’ll assume it is a representative sample. With this, we can easily compute that there are exactly
2302 words in there that translate to
abactinally abrogative absinthol acclimation accumulate acenaphthene achroous acknowledge acriflavine acromegaly ...
foolship are just a few of the ones that I found quite funny in the context of the picture in question.
But what are the odds? Let us assume all these words ended up in
100% bucket - it contains about
0.98% of total words. What about other buckets? Here is what we get if we check the count of all possible buckets.
Data fits normal distribution with parameters:
mean = 112.3882 standard deviation = 40.89031
With this, we see that it’s not that uncommon to end up with a value near
112. Actually, if we permute the way we assign numbers to letters we will end up with a normal distribution as well. This might seems surprising at first, but it makes more sense when you have a look at the distribution of word lengths.
Let us have a look at the distribution of counts with regard to value grouped by length.
Distribution in red reveals that it’s not that uncommon for a word of length
8 to have a value of