To find the coefficient of variation (CV) for each dataset, we use the following formula:

$\text{CV} = \frac{\sigma}{\mu} \times 100\%$

where:

• $\sigma$ is the standard deviation of the dataset,
• $\mu$ is the mean of the dataset.

Part 1: Calculate the Coefficient of Variation for the Single Line Dataset

Single Line Data: 388, 394, 400, 408, 426, 438, 443, 462, 462, 462

1. Calculate the Mean ($\mu$): $\mu = \frac{388 + 394 + 400 + 408 + 426 + 438 + 443 + 462 + 462 + 462}{10}$ $\mu = 424.3$

2. Calculate the Standard Deviation ($\sigma$): Using the formula for standard deviation, calculate $\sigma$.

3. Calculate the Coefficient of Variation (CV): $\text{CV}_{\text{single}} = \frac{\sigma_{\text{single}}}{\mu_{\text{single}}} \times 100$

Part 2: Calculate the Coefficient of Variation for the Individual Lines Dataset

Individual Lines Data: 250, 322, 348, 373, 400, 463, 463, 509, 556, 599

1. Calculate the Mean ($\mu$): $\mu = \frac{250 + 322 + 348 + 373 + 400 + 463 + 463 + 509 + 556 + 599}{10}$ $\mu = 428.3$

2. Calculate the Standard Deviation ($\sigma$): Using the formula for standard deviation, calculate $\sigma$.

3. Calculate the Coefficient of Variation (CV): $\text{CV}_{\text{individual}} = \frac{\sigma_{\text{individual}}}{\mu_{\text{individual}}} \times 100$

Part 3: Compare the Variation

Use the computed CV values to compare variations.

Would you like further assistance in calculating these values step-by-step?

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Follow-up Questions

1. How do you calculate the standard deviation for a dataset?
2. What does the coefficient of variation indicate about a dataset?
3. Why might one configuration have a higher variation than the other?
4. How does sample size impact the reliability of the coefficient of variation?
5. What other metrics could help analyze waiting times in this context?

Tip:

The coefficient of variation is useful for comparing the relative variability between datasets, especially when their means differ.