Homework Soursea Perform 1D Stats on your five masses b Add a one gram syst
a) Perform 1D Stats on your five masses.
b) Add a one gram systematic error by shifting all five your mass values +1g. Repeat your 1D Stats and note what has and has not changed.
c) Reset and add a one gram systematic error to just your first two mass values. Repeat your 1D Stats and note what has and has not changed.
d) From the data alone, do you feel you would have been able to catch these systematic errors?
Section
(g)
(cm)
(cm)
(cm)
(cm)
(cm)
(cm3)
(g/cm3)
1
60.019
2.53
5.04
3.81
2.52
1.905
21.63011
2.774789
2
60.02
3.55
5.13
3.82
2.565
1.91
32.68982
1.836045
3
60.04
2.54
5.1
3.8
2.55
1.9
23.08112
2.60126
4
60.04
2.53
5.06
3.82
2.53
1.91
21.87989
2.744073
5
60.03
3.82
5.1
3.82
2.55
1.91
34.25532
1.752428
| Section | (g) | (cm) | (cm) | (cm) | (cm) | (cm) | (cm3) | (g/cm3) |
| 1 | 60.019 | 2.53 | 5.04 | 3.81 | 2.52 | 1.905 | 21.63011 | 2.774789 |
| 2 | 60.02 | 3.55 | 5.13 | 3.82 | 2.565 | 1.91 | 32.68982 | 1.836045 |
| 3 | 60.04 | 2.54 | 5.1 | 3.8 | 2.55 | 1.9 | 23.08112 | 2.60126 |
| 4 | 60.04 | 2.53 | 5.06 | 3.82 | 2.53 | 1.91 | 21.87989 | 2.744073 |
| 5 | 60.03 | 3.82 | 5.1 | 3.82 | 2.55 | 1.91 | 34.25532 | 1.752428 |
Solution
From the above data, we can say if we will add the systematic error for all the data points, the average value will be increased by the amount what we add, the standrad deviation and the mean error will be unchanged. However it will change the mean value of gm/cm^3 too.
If we will add the systematic error to some specific points, then the average value, error, standard deviation in all the quantities will get changed.
| Section | (g) | (cm) | (cm) | (cm) | (cm) | (cm) | (cm3) | (g/cm3) | Error in mass |
| 1 | 60.019 | 2.53 | 5.04 | 3.81 | 2.52 | 1.905 | 21.63011 | 2.774789 | -0.0108 |
| 2 | 60.02 | 3.55 | 5.13 | 3.82 | 2.565 | 1.91 | 32.68982 | 1.836045 | -0.0098 |
| 3 | 60.04 | 2.54 | 5.1 | 3.8 | 2.55 | 1.9 | 23.08112 | 2.60126 | 0.0102 |
| 4 | 60.04 | 2.53 | 5.06 | 3.82 | 2.53 | 1.91 | 21.87989 | 2.744073 | 0.0102 |
| 5 | 60.03 | 3.82 | 5.1 | 3.82 | 2.55 | 1.91 | 34.25532 | 1.752428 | 0.0002 |
| Average | 60.0298 | 2.994 | 5.086 | 3.814 | 2.543 | 1.907 | 26.707252 | 2.341719 | -1.42109E-15 |
| Error | -1.42109E-15 | ||||||||
| Standard Deviation | 0.010256705 | 0.637989 | 0.035777 | 0.008944 | 0.017889 | 0.004472136 | 6.22483089 | 0.504918304 | |
| here one can see clearly that average error is almost zero. | |||||||||
| Section | (g) | (cm) | (cm) | (cm) | (cm) | (cm) | (cm3) | (g/cm3) | Error in mass |
| 1 | 61.019 | 2.53 | 5.04 | 3.81 | 2.52 | 1.905 | 16.194277 | 3.767936043 | -0.0108 |
| 2 | 61.02 | 3.55 | 5.13 | 3.82 | 2.565 | 1.91 | 44.738875 | 1.363914493 | -0.0098 |
| 3 | 61.04 | 2.54 | 5.1 | 3.8 | 2.55 | 1.9 | 16.387064 | 3.72488934 | 0.0102 |
| 4 | 61.04 | 2.53 | 5.06 | 3.82 | 2.53 | 1.91 | 16.194277 | 3.769232797 | 0.0102 |
| 5 | 61.03 | 3.82 | 5.1 | 3.82 | 2.55 | 1.91 | 55.742968 | 1.094846618 | 0.0002 |
| Average: | 61.0298 | 2.994 | 5.086 | 3.814 | 2.543 | 1.907 | 29.8514922 | 2.744163858 | -1.42109E-15 |
| Mean error = | -1.42109E-15 | ||||||||
| Standard deviation | 0.010256705 | 0.637989 | 0.035777 | 0.008944 | 0.017889 | 0.004472136 | 19.01533964 | 1.386184868 | |
| Section | (g) | (cm) | (cm) | (cm) | (cm) | (cm) | (cm3) | (g/cm3) | Error in mass |
| 1 | 61.019 | 2.53 | 5.04 | 3.81 | 2.52 | 1.905 | 16.194277 | 3.767936043 | 0.5892 |
| 2 | 61.02 | 3.55 | 5.13 | 3.82 | 2.565 | 1.91 | 44.738875 | 1.363914493 | 0.5902 |
| 3 | 60.04 | 2.54 | 5.1 | 3.8 | 2.55 | 1.9 | 16.387064 | 3.663865595 | -0.3898 |
| 4 | 60.04 | 2.53 | 5.06 | 3.82 | 2.53 | 1.91 | 16.194277 | 3.707482588 | -0.3898 |
| 5 | 60.03 | 3.82 | 5.1 | 3.82 | 2.55 | 1.91 | 55.742968 | 1.076907136 | -0.3998 |
| Average: | 60.4298 | 2.994 | 5.086 | 3.814 | 2.543 | 1.907 | 29.8514922 | 2.716021171 | 0 |
| Mean error = | 0 | ||||||||
| Standard deviation | 0.538335583 | 0.637989 | 0.035777 | 0.008944 | 0.017889 | 0.004472136 | 19.01533964 | 1.369563524 |
