How 94% Are Above Average
"Hello Kind Sir/Madame. Question? Do you feel you are above average? Yes or No, please?"
If asked just like that, it is easy to see how 94% answer this question 'yes'. Because it is a completely open question, the answer will be easily be interpretive in a very subjective way.
"Hello Kind Sir/Madame. On a scale of 1-10, what would you rank yourself in general?"
A little different, but depending on the mood of the person, most (probably 94%) will probably say 6 or more.
Over the broad scope of a person's skills and abilities, most people will believe they are above average on most general scales.
Are you an above average student? (Carried good grades, got a degree, sure.)
Are you an above average cook? (No one has died from eating my food, sure.)
Are you an above average writer? (You are reading this, right?)
Are you an above average reader? (I was able to read what I wrote, right?)
Even those, will be answered with a subjective bias based on a person's experience and real-world internal sampling.
Take the question, 'above average cook'? I compare myself to everyone that has ever cooked for me. I may honestly say I am worse than let's say Gordon Ramsey, but I am not answering 'one of the best', I am answering simply, 'above average'. Considering a large percentage of people don't even cook, just by being able to cook scrambled eggs with any skill probably puts you 'above average'.
Again, we process the general 'above average' question to all of our skills, and we decide we are 'above average' (unless you are pragmatic or depressed, then you fall into the other 6%)
Now, as you start to give the people asked a more random survey of things to be 'above-average in', for example:
Cooking, playing football, building an engine, playing poker, winning the lottery, gardening, looks, etc.
Now, you are going to start getting a deeper mix of yes and no answers, and the aggregate percentage will start getting lower.
Take a sample of 100 students. They take a test of 100 questions. The worst student scores 49/100. The rest score 90/100. Against the questions themselves, 99% of the students had a way-above-average understanding of the material. Even against the average score, (89.59/100) The 99 students are still, technically above average because they all have a score of 90.
With just the general question, there is too much wiggle room. Everyone will wiggle upward.
It is not a statistical impossibility, it is a statistically useless question. A trick of the mind and the sample set. A perfect example of how you can use statistics to tell whatever story you want to.