CHEM 2400/2480
Solutions for Problem Set 2: Statistics, error analysis and standard curves
1. The following 10 results are from experimental measurements for the atomic weight of
carbon:
12.0112, 12.0210, 12.0102, 12.0118, 12.0111, 12.0106, 12.0113, 12.0101, 12.0097,
12.0095
Calculate the mean, the average deviation from the mean, and the standard deviation for
these results. Can the outlying point be justifiably rejected? If so, re-calculate an
improved value for the mean and the standard deviation.
mean
deviation from the mean
standard deviation,
outlying pt:
Qcrit = 0.41 at 90% confidence level
since Qexp > Qcrit, reject value, (also at 99%)!
new mean 12.0106, new standard deviation 0.0008 CHEM 2400/2480
2. Calculate the value of the function F and its standard deviation for F defined as:
a. F = X + Y - Z (Ans. -7 ± 4)
b. F = 2X + 3Y - 3Z (Ans. -20 ± 10)
c. F = X/(Y + Z) (Ans. 0.08 ± 0.03)
d. F = 10X - (7Y/Z) (Ans. 9 ± 1)
2
e. F = XY/(Z ) 2 (Ans. 0.02 ± 0.01)
f. F = (X + Y )/Z (Ans. -7 ± 4)
In each case: X = 1.0 ± 0.1; Y = 2.0 ± 0.5; Z = 10 ± 4
a. F = X + Y - Z = 1.0 + 2.0 - 10 = -7.0
b. F = 2X + 3Y - 3Z = -22
c. CHEM 2400/

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