-
We need your support!
We are currently struggling to cover the operational costs of Xtremepapers, as a result we might have to shut this website down. Please donate if we have helped you and help make a difference in other students' lives!
Click here to Donate Now (View Announcement)
Help with uncertainty values and estimations for Physics (AS)
- Thread starter nafeekhan
- Start date
- Messages
- 391
- Reaction score
- 262
- Points
- 43
Uncertainty of a value
In experimental science, whenever we quote a quantitative result, we must be able to indicate the precision of the result, that is to indicate how well we know this result or how confident we are in this result. There are two ways to do this.
1. Use of significant figures alone
When taking a measurement, we write down no more than one uncertain figure. That is a measurement of 83.67 volts would mean the "7" is uncertainty while the "83.6" is certain. In combining these measurements (data) to calculate a result, certain rules tell us how many figures to write in the result. (note this has nothing to do with the convention used in class, that answers are being given to three significant figures). This method of using significant figures alone, while better than nothing, is not really good enough for the lab work in this course. The only time you should use this method is when you are too pressed for time to use the second method.
2. Quoting the Uncertainty
For an example of a voltmeter one might write 51.6 ±0.1 volts. What is the meaning of such a value? If we are doing more careful work, we would repeat the measurement a number of times. The average or mean of our readings is our "best estimate" or value of 51.6. The spread in these readings gives us the uncertainty of ±0.1 in the reading (also referred to as the "error" in the reading).
There are several ways of measuring the spread in the readings. Two of these are mean deviation and standard (r.m.s.) deviation. What they tell us is a probability of finding the result within a certain interval. Under certain assumptions made in statistical theory, we can expect to find about 68% of the readings within one standard deviation and 95% within two standard deviations of the mean for normal distributions.
With lab experiments, measurements are often not repeated and what might be the spread in the measurements is estimated (as if the measurement where repeated a number of times). The estimate of the uncertainty (spread in the measurements) is done as a reasonable guess, influenced by how the measurement was made and by the precision of the instruments used. It does not follow any set rule (often taught is using ½ the least significant decimal place of a number or of the smallest division in the measuring instrument - these types of rules can lead to inappropriate estimates of uncertainty). Keep in mind in your estimations of an uncertainty, uncertainty indicates where most measurements would fall if repeatedly measured.
In experimental science, whenever we quote a quantitative result, we must be able to indicate the precision of the result, that is to indicate how well we know this result or how confident we are in this result. There are two ways to do this.
1. Use of significant figures alone
When taking a measurement, we write down no more than one uncertain figure. That is a measurement of 83.67 volts would mean the "7" is uncertainty while the "83.6" is certain. In combining these measurements (data) to calculate a result, certain rules tell us how many figures to write in the result. (note this has nothing to do with the convention used in class, that answers are being given to three significant figures). This method of using significant figures alone, while better than nothing, is not really good enough for the lab work in this course. The only time you should use this method is when you are too pressed for time to use the second method.
2. Quoting the Uncertainty
For an example of a voltmeter one might write 51.6 ±0.1 volts. What is the meaning of such a value? If we are doing more careful work, we would repeat the measurement a number of times. The average or mean of our readings is our "best estimate" or value of 51.6. The spread in these readings gives us the uncertainty of ±0.1 in the reading (also referred to as the "error" in the reading).
There are several ways of measuring the spread in the readings. Two of these are mean deviation and standard (r.m.s.) deviation. What they tell us is a probability of finding the result within a certain interval. Under certain assumptions made in statistical theory, we can expect to find about 68% of the readings within one standard deviation and 95% within two standard deviations of the mean for normal distributions.
With lab experiments, measurements are often not repeated and what might be the spread in the measurements is estimated (as if the measurement where repeated a number of times). The estimate of the uncertainty (spread in the measurements) is done as a reasonable guess, influenced by how the measurement was made and by the precision of the instruments used. It does not follow any set rule (often taught is using ½ the least significant decimal place of a number or of the smallest division in the measuring instrument - these types of rules can lead to inappropriate estimates of uncertainty). Keep in mind in your estimations of an uncertainty, uncertainty indicates where most measurements would fall if repeatedly measured.