With the small sample set I was talking about, (you, neighbor, and Gates), there wouldn't BE a mode strictly speaking.
Strictly speaking, there is always a mode and in your chosen example there are three modes. You are still making it up as you go along.
https://www.mathsisfun.com/mode.html
More Than One ModeWe can have more than one mode.
Example: {1, 3, 3, 3, 4, 4, 6, 6, 6, 9}3 appears three times, as does 6.
So there are two modes: at 3 and 6
Having two modes is called "bimodal".
Having more than two modes is called "multimodal".
Strictly speaking, in your chosen multimodal example, you woud have three modes, just as I stated. Your example had three modes and was trimodal or multimodal.
I used that example, simply because on my late-night cursory read of your first post, I didn't see N=(about 541?) for the study.
[Woodpusher #310, replying to grey_whiskers #309]
"In this study, 541 individuals were identified who died of fentanyl-induced overdose in New Hampshire from January 1, 2015 to September 30, 2016."
[emphasis in original]
I quoted the report to identify the specific number of individuals in the study and provided a link to the report itself.
Regardless of the number of subjects in the study which I provided, your chosen example would have been useless for demonstrating anything about mode values.
GroupingIn some cases (such as when all values appear the same number of times) the mode is not useful.
Id. You made up an example where mode is not useful. It was not easy to make up an example where mode is not useful, but you were up to the task.
The point is, if you have an extreme outlier within a series of values, then the count of members of the group, which are below the average, is going to be vastly greater than the count of people above the average.
The point is that I supplied data to the real world study, using the same sample size (541), same average value (9.96), the same low value (0.75) and the same outlier high value (113), and proved beyond a reasonable doubt and to a moral and mathematical certainty that your claim is false. If your claim were true, my given example could not exist. But it can and does. The larger the sample size, the less relevant the outlier becomes. I demonstrated, with real values, that the mode and the median could be higher than the mean average value with the four pieces of given data.
But if you think mean and mode are higher math, it shows your low intellectual level.
Mode, mean and median are hardly higher math terms. I dismissively used the term arithmetic. They are actually basic terms used in statistics.
Strictly speaking, there is always a mode and in your chosen example there are three modes. You are still making it up as you go along.
Not making it up, just not typing coherently. The internet does not handle inflections well, and merely emphasizing the word "BE" didn't convey my point. I should have emphasized "A" instead of "BE": not a unique value of the mode, corresponding to one value within the set which is guaranteed to appear more often than all the others.
But that would've been too cumbersome to explain on my third straight night of four hours sleep.
I wasn't making it up, I was remembering. It was a bug I found in someone else's computer program 15 years ago, and led to an eigenvalue subroutine four layers down dying from a divide-by-zero error. I can't remember anymore, but I *think* that series had either 7 or 15 elements in it.