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To solve this problem, we need to calculate the coefficient of variation (CV) for both the single line data set and the individual lines data set. The coefficient of variation is calculated as:

\[
\text{CV} = \left( \frac{\sigma}{\mu} \right) \times 100\%
\]

where:
- \(\sigma\) is the standard deviation of the data set, and
- \(\mu\) is the mean of the data set.

Let's analyze the data provided in the tables for each data set.

### 1. Single Line Data Set
Values: 390, 396, 404, 408, 427, 438, 442, 460, 460, 460

### 2. Individual Lines Data Set
Values: 251, 325, 349, 373, 404, 462, 462, 509, 557, 601

I will calculate the mean and standard deviation for each data set, then use those values to compute the coefficient of variation for each. Let's proceed with the calculations.The calculations yield the following results:

1. **Single Line Data Set:**
   - Mean (\(\mu\)) = 428.5
   - Standard Deviation (\(\sigma\)) = 27.5
   - Coefficient of Variation (CV) ≈ 6.4%

2. **Individual Lines Data Set:**
   - Mean (\(\mu\)) = 429.3
   - Standard Deviation (\(\sigma\)) = 109.1
   - Coefficient of Variation (CV) ≈ 25.4%

### Conclusion
Comparing the CV values:
- The individual lines data set has a significantly higher CV (25.4%) compared to the single line data set (6.4%).
- This implies **Option A** is correct: "The variation of the individual lines is much larger than the variation of the single line because its CV is larger than the CV for the single line data set."

Would you like more details on the calculations or have any questions?

### Related Questions
1. What is the impact of using the coefficient of variation in comparing data sets?
2. How would results differ if the standard deviation was calculated as a population rather than a sample?
3. Can CV be used effectively if the mean of a data set is zero or close to zero?
4. How does the coefficient of variation provide insight in queuing theory and waiting line analysis?
5. How would adding more data points affect the mean, standard deviation, and CV?

### Tip
Remember, the coefficient of variation is especially useful for comparing variability across data sets with different units or means.

A Providence Hospital experiment involves two different waiting line configurations for patients arriving for admission. The waiting times (in seconds) are recorded with a single line configuration that feeds four stations and another configuration with individual lines at the four stations. Find the coefficient of variation for each of the two samples, and then compare the variation.

Learn how to calculate and compare the coefficient of variation for single and individual line configurations in a hospital's patient waiting times. The problem involves determining mean, standard deviation, and CV for two data sets to evaluate variability across different waiting line configurations.

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