Concept explainers
Time to review: The following table presents the time taken to review articles that were submitted for publication to the journal Technometrics during a recent year. A few articles took longer than 9 months to review; these are omitted from the table. Consider the data to be a population.
- Approximate the variance of the times.
- Approximate the standard deviation of the times.
a)
To find the Population variance for given data.
Answer to Problem 39E
Variance = 0.384
Explanation of Solution
Given:
The data
Time (Months) | Number of Articles |
0.0−0.9 | 45 |
1.0−1.9 | 17 |
2.0−2.9 | 18 |
3.0−3.9 | 19 |
4.0−4.9 | 12 |
5.0−5.9 | 14 |
6.0−6.9 | 13 |
7.0−7.9 | 22 |
8.0−8.9 | 11 |
Calculation:
Time (Months) | Number of Articles(fi) | Mid Value(xi) | ||
0.0−0.9 | 45 | 0.5 | 22.5 | 10.27 |
1.0−1.9 | 17 | 1.5 | 25.5 | 4.86 |
2.0−2.9 | 18 | 2.5 | 45 | 1.45 |
3.0−3.9 | 19 | 3.5 | 66.5 | 0.04 |
4.0−4.9 | 12 | 4.5 | 54 | 0.63 |
5.0−5.9 | 14 | 5.5 | 77 | 3.22 |
6.0−6.9 | 13 | 6.5 | 84.5 | 7.81 |
7.0−7.9 | 22 | 7.5 | 165 | 14.40 |
8.0−8.9 | 11 | 8.5 | 93.5 | 23.00 |
Sum | 171 | 633.50 | 65.69 | |
Mean | 3.70 |
The variance for the given data is 0.384.
b)
To find the Population standard deviation for given data.
Answer to Problem 39E
Standard deviation = 0.62
Explanation of Solution
Calculation:
Time (Months) | Number of Articles(fi) | Mid Value(xi) | ||
0.0−0.9 | 45 | 0.5 | 22.5 | 10.27 |
1.0−1.9 | 17 | 1.5 | 25.5 | 4.86 |
2.0−2.9 | 18 | 2.5 | 45 | 1.45 |
3.0−3.9 | 19 | 3.5 | 66.5 | 0.04 |
4.0−4.9 | 12 | 4.5 | 54 | 0.63 |
5.0−5.9 | 14 | 5.5 | 77 | 3.22 |
6.0−6.9 | 13 | 6.5 | 84.5 | 7.81 |
7.0−7.9 | 22 | 7.5 | 165 | 14.40 |
8.0−8.9 | 11 | 8.5 | 93.5 | 23.00 |
Sum | 171 | 633.50 | 65.69 | |
Mean | 3.70 |
The Standard deviation for the given data is 0.62.
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Chapter 3 Solutions
Elementary Statistics 2nd Edition
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