Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation.

Bank A​ (single line):

6.56.5

nbsp 6.6  6.6

nbsp 6.7  6.7

nbsp 6.8  6.8

nbsp 7.0  7.0

nbsp 7.3  7.3

nbsp 7.4  7.4

nbsp 7.6  7.6

nbsp 7.6  7.6

nbsp 7.7  7.7
 
Bank B​ (individual lines):

4.44.4

nbsp 5.4  5.4

nbsp 5.8  5.8

nbsp 6.2  6.2

nbsp 6.7  6.7

nbsp 7.7  7.7

nbsp 7.7  7.7

nbsp 8.5  8.5

nbsp 9.3  9.3

nbsp 9.7  9.7

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Part 1

The coefficient of variation for the waiting times at Bank A is 

enter your response here​%.

​(Round to one decimal place as​ needed.)

To find the coefficient of variation (CV) for the waiting times at each bank, we will follow the same steps:

\[
\text{Coefficient of Variation (CV)} = \left(\frac{\text{Standard Deviation}}{\text{Mean}}\right) \times 100\%
\]

### Step 1: Organize the data.

- **Bank A (Single Line)**: 6.5, 6.6, 6.7, 6.8, 7.0, 7.3, 7.4, 7.6, 7.6, 7.7
- **Bank B (Individual Lines)**: 4.4, 5.4, 5.8, 6.2, 6.7, 7.7, 7.7, 8.5, 9.3, 9.7

### Step 2: Calculate the CV for each bank.

Let's compute these values step-by-step.The coefficients of variation for the waiting times are:

- **Bank A (Single Line):** \( 6.4\% \) (rounded to one decimal place)
- **Bank B (Individual Lines):** \( 24.3\% \) (rounded to one decimal place)

### Comparison:
Bank B has a much higher coefficient of variation compared to Bank A, indicating that the waiting times at Bank B are more variable and less consistent than those at Bank A.

Would you like more details or have any questions?

### Related Questions:
1. What factors could contribute to the higher variation in waiting times at Bank B?
2. How does a higher CV impact customer satisfaction in waiting lines?
3. Can other statistical measures help understand the difference between these two banks?
4. How could banks reduce waiting time variability?
5. Why is the coefficient of variation a useful metric in this context?

**Tip:** A high CV suggests inconsistency, which may be problematic in customer service environments, as it can lead to dissatisfaction.

Learn how to calculate and compare the coefficient of variation (CV) for waiting times at two banks: one with a single waiting line (Bank A) and another with individual lines (Bank B). Understand how CV measures variability and its implications for customer service and satisfaction.

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