So let me start by saying that the significant majority of people are absolutely terrible at working with statistics. Part of the problem is that people just don’t like math, and part of the problem is the cognitive biases that enter into actual implementations in real-world situations, but another part of the problem is that the education system just doesn’t teach you what you need to know.
For example, most intro-level probability courses (which are all your average person ever takes) will teach you about the mean, median, and mode. The mean of a distribution is what we more commonly refer to as the average. The mode is the most frequently-occurring result, and the median is the result that lies right in the middle of the distribution. But if I add 14 plus the rolls of two 6-sided dice (abbreviated as 2d6 + 14) and compare this to adding the rolls of two 20-sided dice (abbreviated as 2d20), I will find that the two distributions have the same mean, median, and mode (all of which are 21). So your average person has no idea how to mathematically describe the difference between 2d6 + 14 and 2d20 (though the average Dungeons and Dragons player might). The statistical concept required to differentiate the two actions just isn’t taught at an introductory level.
Furthermore, when you get into real statistics the median and the mode are mostly ignored. The mean (which, despite the terminology introduced in your high-school classes is actually referred to as the average by everyone I’ve ever worked with) is used all the time, but nobody cares about the median and the mode. (Though now that I think about it, this may be because with a Gaussian or Normal distribution, mean = median = mode, and there’s no use giving someone the same information three times.)
What people do care about, in addition to the mean, is a number called the standard deviation. This is a number that represents the spread of outcomes in a distribution. While 2d6 + 14 and 2d20 have the same mean, median, and mode, they have very different standard deviations. This is because the possible outcomes of 2d20 range from 2 to 40, while the possible outcomes for 2d6 + 14 range only from 16 to 26. So while the two distributions have the same average, the same most likely outcome, and the same middle outcome, the possible outcomes in 2d6 + 14 are grouped much more closely together, while the possible outcomes in 2d20 are more spread out.
The standard deviation is more difficult to calculate than the mean, median, and mode (which is probably why it’s left out of introductory courses). Mathematically, it’s the difference between the average of “outcome squared” and the square of “average outcome.” But you don’t actually need to be able to calculate standard deviations to understand what I want to say about discrimination. All you need to know is what a standard deviation represents, and that’s the spread of possibilities. The larger the standard deviation, the larger the spread.
This is easier to see graphically, so here you go: Two graphs representing the distribution of 2d6 + 14 versus 2d20.