And the majority of people are average. That's why it's called an average.
No. An average, or a mean, measures the central tendency of a group of numbers; this does not imply that most people are in the center, it implied that the mean of the sample is concentrated there. How "smart" varies greatly from person to person, there isn't a clearly definitive pattern. There are a lot of outliers, meaning that an average is pretty useless for guessing the intelligence of a random person plucked off of the street.
I'm using average as a synonym for usual. Usual=most common
If you look at a graph like this 68% of people have around average intelligence. That's a majority of people.
Hold the fuck up right there, that's not what average means and that's not quite how standard/normal/Gaussian distributions work.
As you should know there are three kinds of averages, mean, median, mode, all of which provide information about a given sample, but provide very different kinds of information. Let's look at a sample of 101 people who took a test which gives a number as a result (say an intelligence test).
The mean is the common definition of average; you add up all 101 scores then divide the answer by 101; this works well provided all the scores are numerically close together, but doesn't distinguish between different clusters; for instance, if 51 people scored 10 and 50 people scored 90, then the mean is 49.6, despite
nobody having that score, or anything close to it.
The median gives a rough idea of a middle value; if you take all 101 results and order them from smallest to largest, then the median is result number 51, the middle of the set. This tells us that half the people in the set scored lower than or equal to #51, and half scored higher than or equal to #51; using the example before the median is 10; half the remaining people scored exactly that, and the other half scored greater than that; so the median can partition the population into "below average" and "above average" but it doesn't say anything else.
The third average is the mode, the number the occurs most frequently, to illustrate i'll use a better set: {1,1,1,2,3,3,4,4,4,4,5,5,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9}
The mode in this case is 8 because it shows up the most; the mode alone says nothing about how frequent this result is, how much more frequent it is than others, and it doesn't even say if it's the majority, but you can do something interesting, removing all the values that are equal to the mode you get another set:
{1,1,1,2,3,3,4,4,4,4,5,5,6,6,7,7,7,9}
In which case the mode is 4; repeating this process you can order the size of different groups, though it alone says nothing about how large those groups are.
The point to realize is that
this is really basic stats here, everyone who can count should already know this; and if you are going to talk maths, make sure you know your definitions.
Now what's not quite basic stats, but still fairly basic is the graph you posted, the Gaussian distribution has the property that all three averages are the same, mean = median = mode
But here's the catch that I've been building up to; if that graph represent intelligence, and you pick a random person, what's the probability that they're average?
ZeroIf you try to calculate the probability of a person being exactly one intelligence value, you need to integrate a probability function from one value of x (intelligence in this case) to the exact same value of x, and for any function the answer is always zero. (you should know elementary calculus by now)
What you can do is integrate between different values of intelligence and say: " there's a 34.1% chance that your IQ is between 100 and 115" but if you try to narrow the range , say between IQ 99 and 101, then the probability drops to almost nothing and the answer becomes meaningless.
TL;DR Do some maths egg.
EDIT: The corollary being that effectively no one is average.
The Above Average Effect