Quote: Original post by nullsquared

Quote: Original post by phantom
Thus following on from that, using standard rounding rules, the answer would be 3:13.

I don't understand these "standard rounding rules."

If event A happens at 6:50 and you're asked at which hour this event happens, it would be at the 6th hour, not the 7th hour.

Without context, I'd say something happening at 6:50 is happening at 7, the 8th hour.

Quote: Original post by nilkn
In my completely anecdotal experience, I've noticed that there's a correlation between incompetence in a teacher and the teacher's unwillingness to compromise with students and listen to their ideas. For instance, I haven't had any problems like this with tenured professors, but I've had more problems like this than I can count on one hand with graduate student teachers. Am I the only one who has noticed this correlation?

I've noticed that tenured professors are pretty easy to get on with. I've only had one class taught by a grad student and she was pretty good, so I can't comment on that side. Non-tenured professors who don't get on well with students don't usually stick around very long so I haven't had to deal with them for more than a semester.

I've also noticed that even easy going professors have at least a few students with these sorts of complaints. My experience is that in these sorts of issues the arrogance tends to be the student's, not the professor's. High school is a little different because the teacher's more likely to give in in the name of the student's self-esteem whereas, in college, they're less likely to care about your wounded pride.

Quote: Original post by Way Walker
Without context, I'd say something happening at 6:50 is happening at 7, the 8th hour.

But the 8th hour is in the range 7 -> 8, isn't it ? And 6:50 isn't even in that range. It doesn't sound right to me to say that 6:50 is in the 8th hour.

Y.

I think you are leaving out some important information that might let us see the teacher's side of the story. For example, if all you are given is that f(6.2108) = 25, then why do you have on your graph that f(x) > 25 when x > 6.2108? I think you should post the exact question and all the details.

Quote: Original post by nullsquared

The problem said specifically "at what time (hour and minute) will f(x) = 25"

As stated, I would say you are correct. The question itself appears to be incorrectly worded. From the given information, we cannot conclude that f(x)=25 at any hour and minute, only that f(x)=25 during the 3rd hour, 13th minute, i.e. during the minute of 3:12. I cannot imagine any justification for rounding.

Quote: Original post by Melekor
I think you are leaving out some important information that might let us see the teacher's side of the story. For example, if all you are given is that f(6.2108) = 25, then why do you have on your graph that f(x) > 25 when x > 6.2108? I think you should post the exact question and all the details.

Quote: Original post by nullsquared

The problem said specifically "at what time (hour and minute) will f(x) = 25"

As stated, I would say you are correct. The question itself appears to be incorrectly worded. From the given information, we cannot conclude that f(x)=25 at any hour and minute, only that f(x)=25 during the 3rd hour, 13th minute, i.e. during the minute of 3:12. I cannot imagine any justification for rounding.

Round up if you need to make sure something's finished (e.g. coming back in 15 minutes for a 12 minute download)

Round down if you need to need to act before something's finished (e.g. finishing by 2:00 to get to your meeting at 2:15)

Round to the nearest if you're just saying the time (e.g. if it's 6:50, it's better to tell me it's 7 o'clock than 6)

For the current question, where it'll be 25 at precisely 3 hours, 12 minutes, 38.88 seconds, does the context suggest that it's better to be 40 seconds too early (round down), 20 seconds too late (round up), or does it not really matter (round nearest, or take your pick because it doesn't really matter)?

Quote: Original post by Way Walker
Round to the nearest if you're just saying the time (e.g. if it's 6:50, it's better to tell me it's 7 o'clock than 6)

Except when you don't, which is almost always the case with units of time finer than hours. Like I said earlier, a digital clock that only expresses the time in minutes invariably rounds down. If it rounded up, the only good that would do is to make it 30 seconds off. People are used to assuming that a digital clock will change from 8:59 to 9:00 only when it is actually 9:00.

Quote: Original post by cowsarenotevil

Quote: Original post by Way Walker
Round to the nearest if you're just saying the time (e.g. if it's 6:50, it's better to tell me it's 7 o'clock than 6)

Except when you don't, which is almost always the case with units of time finer than hours. Like I said earlier, a digital clock that only expresses the time in minutes invariably rounds down. If it rounded up, the only good that would do is to make it 30 seconds off. People are used to assuming that a digital clock will change from 8:59 to 9:00 only when it is actually 9:00.

And an analog clock without a seconds hand will give the visual appearance of rounding to the nearest.

Ignoring the fact that you can only really rely on clocks to be within a couple minutes of the "actual" time, you could also say that rounding to the nearest would never be off by more than 30 seconds (about 15 on average) while rounding down would never be off by more than 60 seconds (about 30 on average). Also, I don't think anyone would bat an eye if you told them it was "4:25" when the display actually read "4:24:40".

Round to the nearest if you're most concerned with the actual amount of time, but round up or down if you need an upper or lower bound on how much time has past.

Quote: Original post by Way Walker
And an analog clock without a seconds hand will give the visual appearance of rounding to the nearest.

I don't see how this is "rounding." It gives you more precision; it doesn't actually jump to the new minute earlier.

Quote: Ignoring the fact that you can only really rely on clocks to be within a couple minutes of the "actual" time, you could also say that rounding to the nearest would never be off by more than 30 seconds (about 15 on average) while rounding down would never be off by more than 60 seconds (about 30 on average).

This is really circular logic. In both cases you only know the "answer" within a 60-second range. Rounding doesn't change that.

Quote: Also, I don't think anyone would bat an eye if you told them it was "4:25" when the display actually read "4:24:40".

Yes, but if I had a clock that was supposed to be extremely accurate by synchronizing with whatever and it always changed minutes 30 seconds earlier than every other clock I would probably be frustrated.

You can make a case for rounding when you are measuring the time between two events, because then you actually are going to get a more accurate answer. But when you're just telling time, the only thing you are doing is making your clock 30 seconds off. That's why clocks don't do it, ever.

This reminds me of an episode I had in the 6th grade.

English class just ended for the day, and we had received our graded spelling tests. Noticing that one of the correct words on my test was marked wrong, I proceeded to pointed it out to the teacher. She admitted I was right but refused to correct it, citing something to the effect of, "You already have 100," referring to my 100+ grade.

This still bothers me, over a decade later.

Quote: Original post by cowsarenotevil

Quote: Original post by Way Walker
And an analog clock without a seconds hand will give the visual appearance of rounding to the nearest.

I don't see how this is "rounding." It gives you more precision; it doesn't actually jump to the new minute earlier.

Because 3:14:50 is practically indistinguishable from 3:15:05 without a seconds hand.

Quote:

Quote: Ignoring the fact that you can only really rely on clocks to be within a couple minutes of the "actual" time, you could also say that rounding to the nearest would never be off by more than 30 seconds (about 15 on average) while rounding down would never be off by more than 60 seconds (about 30 on average).

This is really circular logic. In both cases you only know the "answer" within a 60-second range. Rounding doesn't change that.

Where's the circle in my reasoning? I'm just using the definition of absolute error |tmeasured-tactual|. You're right that they have the same precision (time is known to within 60 seconds) but one is more accurate than the other (the mean of all times measuring 3:15 is 3:15 for one but 3:14:30 for the other).

I'm not disagreeing that my scheme will be off by 30 seconds from truncation which is the most common convention for digital clocks. However, rounding to the nearest is very common when telling someone the time (when the proper information is available), is the immediately apparent time from analog clocks, is likely the most common way to measure the length of some process (as in the OP), and is more accurate (but not more precise).

What a pedantic little dick move, teacher. The student makes a good effort to answer the question and you are going to mark it *wrong* because of an argument about rounding? Inspiring stuff.