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> Would you then argue that there are infinitely many medians in this data set By the definition I usually go by (the one with the inequalities), that dataset

by qsort 4y ago

> Would you then argue that there are infinitely many medians in this data set By the definition I usually go by (the one with the inequalities), that dataset has infinitely many medians. There is no reason to say the midpoint is privileged. This is a better definition because it also works on sets where an order is defined but the arithmetic mean is not. If asked to report a single value with no qualifications, I would report either extreme of the interval.

d1sxeyes 4y ago
> There is no reason to say the midpoint is privileged. This is a matter of opinion. I agree it's not 'privileged', but it sacrifices a minimal amount of accuracy for a usable answer. > If asked to report a single value with no qualifications, I would report either extreme of the interval. That's a very interesting answer - so for my contrived example of 18, 20, 25, 30, [35, 40], 45, 50, 55, 60, you would report 35 or 40? How about if I change the dataset a bit (so it's even more contrived): 18, 18, 18, 18, [18, 60], 60, 60, 60, 60 - would you still report either 18 or 60 (again, asking without qualifications)? I think most people would agree that the median calculated as the arithmetic mean of the two middle values (39) is misleading, but that it is less misleading than ignoring half of the data set. How would you respond to that?
- qsort 4y ago
  > you would report 35 or 40? Generally I report the lower end because it more easily generalizes to different quantiles. > How about if I change the dataset a bit would you still report either 18 or 60 (again, asking without qualifications)? Yes. I don't see how answering 39 is any better in that case. > How would you respond to that? I would respond that you should look at the distribution. Reporting the median is particularly misleading in the case of bimodal distributions. I would try to explain that summary statistics are to be taken with caution, possibly showing a picture.
  - hgsgm 4y ago
  - d1sxeyes 4y ago
    > Yes. I don't see how answering 39 is any better in that case. Fair enough. I think 39 would show there's no bias towards younger or older employees. I think 39 is better but I can see both sides of the argument, and can ultimately see that it boils down to a question of personal preference as to which of two wrong answers is 'less wrong'.

by qsort 4y ago

d1sxeyes 4y ago

> There is no reason to say the midpoint is privileged. This is a matter of opinion. I agree it's not 'privileged', but it sacrifices a minimal amount of accuracy for a usable answer. > If asked to report a single value with no qualifications, I would report either extreme of the interval. That's a very interesting answer - so for my contrived example of 18, 20, 25, 30, [35, 40], 45, 50, 55, 60, you would report 35 or 40? How about if I change the dataset a bit (so it's even more contrived): 18, 18, 18, 18, [18, 60], 60, 60, 60, 60 - would you still report either 18 or 60 (again, asking without qualifications)? I think most people would agree that the median calculated as the arithmetic mean of the two middle values (39) is misleading, but that it is less misleading than ignoring half of the data set. How would you respond to that?

qsort 4y ago
> you would report 35 or 40? Generally I report the lower end because it more easily generalizes to different quantiles. > How about if I change the dataset a bit would you still report either 18 or 60 (again, asking without qualifications)? Yes. I don't see how answering 39 is any better in that case. > How would you respond to that? I would respond that you should look at the distribution. Reporting the median is particularly misleading in the case of bimodal distributions. I would try to explain that summary statistics are to be taken with caution, possibly showing a picture.
- hgsgm 4y ago
- d1sxeyes 4y ago
  > Yes. I don't see how answering 39 is any better in that case. Fair enough. I think 39 would show there's no bias towards younger or older employees. I think 39 is better but I can see both sides of the argument, and can ultimately see that it boils down to a question of personal preference as to which of two wrong answers is 'less wrong'.