Attitude - coincidence or not?

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 100%.

abactinally
abrogative
absinthol
acclimation
accumulate
acenaphthene
achroous
acknowledge
acriflavine
acromegaly
...

immature, grumpy, unclever and 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 100.