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My thoughts on number rounding

dylancatlow
Posts: 13,065
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4/20/2013 11:12:47 AM
Posted: 4 years ago
Whenever an accurate figure is desired, and rounding is necessary, wouldn't rounding a non-siginifcant figure to five rather than zero better reflect the true value? For instance, say I have a scale and I want to weigh myself. The scale is only accurate to the nearest 10 pounds. I weight myself and it spits out 170 pounds. Because it's accurate only to the nearest ten pounds, I could also weigh 171, 172, 173, 174, 175, 176, 177, 178 or 179 pounds. Because each of these is equally likely, and a single number needs to represent these possibilities, wouldn't it make sense to take the average of them, and choose the statistically 'least wrong' number, e.g. 175?
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dylancatlow
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4/20/2013 11:13:50 AM
Posted: 4 years ago
Wait, never mind, I just realized that it goes to 169, 168....
"In case anyone hasn't noticed it, the West is in extremis. The undertaker is checking his watch at the foot of its bed, and there's a sinister kettle of croaking, money-feathered vultures on the roof."
dylancatlow
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4/20/2013 11:20:06 AM
Posted: 4 years ago
Pay no nevermind to my previous post, actually. It's still relevant.
"In case anyone hasn't noticed it, the West is in extremis. The undertaker is checking his watch at the foot of its bed, and there's a sinister kettle of croaking, money-feathered vultures on the roof."
Subutai
Posts: 4,090
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4/20/2013 11:43:58 AM
Posted: 4 years ago
That scale would read 170 if you weighed 165-175 pounds, not 170-180.
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dylancatlow
Posts: 13,065
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4/20/2013 11:52:17 AM
Posted: 4 years ago
At 4/20/2013 11:43:58 AM, Subutai wrote:
That scale would read 170 if you weighed 165-175 pounds, not 170-180.

It depends on the kind of scale. If the scale just compared your weight to 10 pound increments, and indicated at which point you weighed the same or more than 170 but not more than 180, then what I'm saying would be relevant.
"In case anyone hasn't noticed it, the West is in extremis. The undertaker is checking his watch at the foot of its bed, and there's a sinister kettle of croaking, money-feathered vultures on the roof."
F-16_Fighting_Falcon
Posts: 18,337
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4/20/2013 1:22:27 PM
Posted: 4 years ago
At 4/20/2013 11:52:17 AM, dylancatlow wrote:
At 4/20/2013 11:43:58 AM, Subutai wrote:
That scale would read 170 if you weighed 165-175 pounds, not 170-180.

It depends on the kind of scale. If the scale just compared your weight to 10 pound increments, and indicated at which point you weighed the same or more than 170 but not more than 180, then what I'm saying would be relevant.

Then, it would be an unusually sucky scale.
Andromeda_Z
Posts: 4,236
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4/21/2013 1:19:03 AM
Posted: 4 years ago
No, in that case it would be best to say 170 (" 10) pounds. This shows both the reading and the amount of uncertainty. Well, not really, because the last digit is just so completely uncertain that you should use scientific notation and drop it entirely, but you get the idea. The scale gave you a reading and that reading is useful. But, so is the uncertainty.
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Subutai
Posts: 4,090
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4/21/2013 3:14:03 PM
Posted: 4 years ago
At 4/20/2013 11:52:17 AM, dylancatlow wrote:
At 4/20/2013 11:43:58 AM, Subutai wrote:
That scale would read 170 if you weighed 165-175 pounds, not 170-180.

It depends on the kind of scale. If the scale just compared your weight to 10 pound increments, and indicated at which point you weighed the same or more than 170 but not more than 180, then what I'm saying would be relevant.

Then that scale doesn't really know rounding in the first place. If it goes by ten-pound increments, then a particular scale reading should encompass weights from 5 pounds below the reading to 5 pounds above the reading, not solely 10 pounds above the reading.
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R0b1Billion
Posts: 3,932
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4/21/2013 10:03:51 PM
Posted: 4 years ago
Rounding is important for scientific calculations, where a failure to do so would represent a misleading level of accuracy for your calculations. If you weight 150 pounds, you don't want to insinuate it's necessarily 150.0
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darkkermit
Posts: 11,204
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4/21/2013 10:07:11 PM
Posted: 4 years ago
Generally if you say that something is off, you use +/-. So it would be 170 +/- 10 pounds.

Also, the degree of accuracy is give in standard deviations. SO one standard deviation can be 5 pounds, so its 170 +/- (two standard deviations) +/-10 pounds.
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Andromeda_Z
Posts: 4,236
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4/21/2013 10:31:28 PM
Posted: 4 years ago
At 4/21/2013 1:19:03 AM, Andromeda_Z wrote:
No, in that case it would be best to say 170 (" 10) pounds. This shows both the reading and the amount of uncertainty. Well, not really, because the last digit is just so completely uncertain that you should use scientific notation and drop it entirely, but you get the idea. The scale gave you a reading and that reading is useful. But, so is the uncertainty.

Ugh 17 +/- 10 pounds. I didn't realize that got messed up until now...
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darkkermit
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4/21/2013 10:36:43 PM
Posted: 4 years ago
At 4/21/2013 10:31:28 PM, Andromeda_Z wrote:
At 4/21/2013 1:19:03 AM, Andromeda_Z wrote:
No, in that case it would be best to say 170 (" 10) pounds. This shows both the reading and the amount of uncertainty. Well, not really, because the last digit is just so completely uncertain that you should use scientific notation and drop it entirely, but you get the idea. The scale gave you a reading and that reading is useful. But, so is the uncertainty.

Ugh 170 +/- 10 pounds. I didn't realize that got messed up until now...

fixed. You still messed it up :p
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Andromeda_Z
Posts: 4,236
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4/21/2013 11:52:45 PM
Posted: 4 years ago
At 4/21/2013 10:36:43 PM, darkkermit wrote:
At 4/21/2013 10:31:28 PM, Andromeda_Z wrote:
At 4/21/2013 1:19:03 AM, Andromeda_Z wrote:
No, in that case it would be best to say 170 (" 10) pounds. This shows both the reading and the amount of uncertainty. Well, not really, because the last digit is just so completely uncertain that you should use scientific notation and drop it entirely, but you get the idea. The scale gave you a reading and that reading is useful. But, so is the uncertainty.

Ugh 170 +/- 10 pounds. I didn't realize that got messed up until now...

fixed. You still messed it up :p

Well, this is awkward...
Don't take me too seriously plz, i'm rarely on here sober