
(a)
Interpretation:
The table for the replicate measurements is given below-
A | B | C | D |
61.25 | 3.27 | 12.06 | 1.9 |
61.33 | 3.26 | 12.14 | 1.5 |
61.12 | 3.24 | 1.6 | |
3.24 | 1.4 | ||
3.28 | |||
3.23 |
The value of mean and number of degree of freedoms associated with the calculation of the mean needs to be determined.
Concept Introduction :
The mean can be calculated using the following formula:
Or
Here, degree of freedom = N
(a)

Answer to Problem A1.1QAP
For set A −
Mean = 61.43
Degree of freedom = 3
For set B −
Mean = 3.25
Degree of freedom = 6
For set C −
Mean = 12.1
Degree of freedom = 2
For set D −
Mean = 2.65
Degree of freedom = 4
Explanation of Solution
The following formula will be used for the calculation of the mean-
Or
Now the mean value for set A-
Degree of freedom for set A = 3
Mean value for set B-
Degree of freedom for set B = 6
Mean value for set C-
Degree of freedom for set C = 2
Mean value for set D −
Degree for freedom for set D = 4
(b)
Interpretation:
The table for the replicate measurements is given below-
A | B | C | D |
61.25 | 3.27 | 12.06 | 1.9 |
61.33 | 3.26 | 12.14 | 1.5 |
61.12 | 3.24 | 1.6 | |
3.24 | 1.4 | ||
3.28 | |||
3.23 |
The value of standard deviation and number of degree of freedoms associated with the calculation of the standard deviation needs to be determined.
Concept Introduction :
The value of standard deviation can be calculated as follows:
Here,
Degree of freedom =
(b)

Answer to Problem A1.1QAP
For set A −
Standard deviation = 0.11
Degree of freedom = 2
For set B −
Standard deviation = 0.02
Degree of freedom = 5
For set C −
Standard deviation = 0.06
Degree of freedom = 1
For set D −
Standard deviation = 0.21
Degree of freedom = 3
Explanation of Solution
The following formula will be used for the calculation of standard deviation −
For set A-
Samples | ||
1 | 61.25 | 3776.1025 |
2 | 61.33 | 3785.9409 |
3 | 61.12 | 3760.1424 |
Put the values,
Degree of freedom for standard deviation =
For set B-
Samples | ||
1 | 3.27 | 10.6929 |
2 | 3.26 | 10.6276 |
3 | 3.24 | 10.4976 |
4 | 3.24 | 10.4976 |
5 | 3.28 | 10.7584 |
6 | 3.23 | 10.4329 |
Put the values,
Degree of freedom for standard deviation =
For set C-
Samples | ||
1 | 12.06 | 145.4436 |
2 | 12.14 | 147.3796 |
Put the values,
Degree of freedom for standard deviation =
For set D-
Samples | ||
1 | 1.9 | 7.29 |
2 | 1.5 | 5.76 |
3 | 1.6 | 6.76 |
4 | 1.4 | 8.41 |
Put the values,
Degree of freedom for standard deviation =
(c)
Interpretation:
The table for the replicate measurements is given below-
A | B | C | D |
61.25 | 3.27 | 12.06 | 1.9 |
61.33 | 3.26 | 12.14 | 1.5 |
61.12 | 3.24 | 1.6 | |
3.24 | 1.4 | ||
3.28 | |||
3.23 |
The coefficient of variation for each set is to be determined.
Concept Introduction :
The following formula will be used for the calculation of the coefficient of variation-
Here,
s = standard deviation
(c)

Answer to Problem A1.1QAP
The coefficient of variation for set A = 0.17%
The coefficient of variation for set B = 0.61%
The coefficient of variation for set C = 0.49%
The coefficient of variation for set D = 7.9%
Explanation of Solution
For set A −
Given that-
s = 0.11
Put the above value,
For set B −
Given that-
s = 0.02
Put the above value,
For set C −
Given that-
s = 0.06
Put the above value,
For set D −
Given that-
s = 0.21
Put the above value,
(d)
Interpretation:
The table for the replicate measurements is given below-
A | B | C | D |
61.25 | 3.27 | 12.06 | 1.9 |
61.33 | 3.26 | 12.14 | 1.5 |
61.12 | 3.24 | 1.6 | |
3.24 | 1.4 | ||
3.28 | |||
3.23 |
The standard error of mean for each set is to be determined.
Concept Introduction:
The following formula will be used for the calculation of the standard error for the mean-
Here,
Standard deviation = s
Degree of freedom = N
(d)

Answer to Problem A1.1QAP
The standard error for mean for set A = 0.063
The standard error for mean for set B = 0.008
The standard error for mean for set C = 0.042
The standard error for mean for set D = 0.10
Explanation of Solution
For set A-
Given that-
Standard deviation = 0.11
Degree of freedom = 3
Put the above values,
For set B-
Given that-
Standard deviation = 0.02
Degree of freedom = 6
Put the above values,
For set C-
Given that-
Standard deviation = 0.06
Degree of freedom = 2
Put the above values,
For set D-
Given that-
Standard deviation = 0.21
Degree of freedom = 4
Put the above values,
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Chapter A1 Solutions
Principles of Instrumental Analysis
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