Concept explainers
The content of liquid detergent bottles is being analyzed. Twelve bottles, randomly selected from the process, are measured, and the results are as follows (in fluid ounces): 16.05, 16.03, 16.02, 16.04, 16.05, 16.01, 16.02, 16.02, 16.03, 16.01, 16.00, 16.07
- (a) Calculate the sample average.
- (b) Calculate the sample standard deviation.
a.
Calculate the sample average.
Answer to Problem 1E
The sample average is 16.029.
Explanation of Solution
Calculation:
Sample average:
Let
Consider the sample average for the given observations,
b.
Calculate the sample standard deviation.
Answer to Problem 1E
The sample standard deviation is 0.0202.
Explanation of Solution
Calculation:
Sample standard deviation:
Let
Consider,
xi | ||
16.05 | 0.021 | 0.0004 |
16.03 | 0.001 | 0.0000 |
16.02 | ̶ 0.009 | 0.0001 |
16.04 | 0.011 | 0.0001 |
16.05 | 0.021 | 0.0004 |
16.01 | ̶ 0.019 | 0.0004 |
16.02 | ̶ 0.009 | 0.0001 |
16.02 | ̶ 0.009 | 0.0001 |
16.03 | 0.001 | 0.0000 |
16.01 | ̶ 0.019 | 0.0004 |
16 | ̶ 0.029 | 0.0008 |
16.07 | 0.041 | 0.0017 |
Therefore,
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