Find the coefficient of variation for each of the two sets of data, then compare the variation.

Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all customers enter a single waiting line) and the Bank of Providence (where customers wait in individual lines at three different teller windows) are listed below.

Jefferson Valley (single line): 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7

Providence (individual lines): 4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0

Jefferson Valley (single line):
Mean: Answer 1 Question 3 minutes.
Standard Deviation: Answer 2 Question 3 minutes.
Coefficient of Variation: Answer 3 Question 3 %.
Providence (individual lines):
Mean: Answer 4 Question 3 minutes.
Standard Deviation: Answer 5 Question 3 minutes.
Coefficient of Variation: Answer 6 Question 3 %.

True of False

Waiting times of customers at the Jefferson Valley Bank have more variation than the waiting times at the Bank of Providence. Answer 7 Question 3
There is an obvious time saving when using a multiple line compared to using a single line for your clients at the bank. Answer 8 Question 3

To find the coefficient of variation for each set of data, we will calculate the mean, standard deviation, and then the coefficient of variation for both the Jefferson Valley Bank and the Bank of Providence.

### Jefferson Valley Bank (Single Line)
**Data Set:** 6.5, 6.6, 6.7, 6.8, 7.1, 7.3, 7.4, 7.7, 7.7, 7.7

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{\sum x_i}{n} = \frac{6.5 + 6.6 + 6.7 + 6.8 + 7.1 + 7.3 + 7.4 + 7.7 + 7.7 + 7.7}{10} = \frac{71.5}{10} = 7.15 \text{ minutes}
\]

#### Step 2: Calculate the Standard Deviation
\[
\text{Variance} = \frac{\sum (x_i - \mu)^2}{n} = \frac{(6.5-7.15)^2 + (6.6-7.15)^2 + \ldots + (7.7-7.15)^2}{10}
\]
\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]
I'll calculate this value now.

#### Step 3: Calculate the Coefficient of Variation
\[
\text{Coefficient of Variation (CV)} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\%
\]

### Bank of Providence (Individual Lines)
**Data Set:** 4.2, 5.4, 5.8, 6.2, 6.7, 7.7, 7.7, 8.5, 9.3, 10.0

#### Step 1: Calculate the Mean
\[
\text{Mean} = \frac{\sum x_i}{n} = \frac{4.2 + 5.4 + 5.8 + 6.2 + 6.7 + 7.7 + 7.7 + 8.5 + 9.3 + 10.0}{10} = \frac{71.5}{10} = 7.15 \text{ minutes}
\]

#### Step 2: Calculate the Standard Deviation
\[
\text{Variance} = \frac{\sum (x_i - \mu)^2}{n} = \frac{(4.2-7.15)^2 + (5.4-7.15)^2 + \ldots + (10.0-7.15)^2}{10}
\]
\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]
I'll calculate this value now.

#### Step 3: Calculate the Coefficient of Variation
\[
\text{Coefficient of Variation (CV)} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\%
\]

Let's compute these values for both sets of data.Here are the results:

### Jefferson Valley Bank (Single Line)
- **Mean:** 7.15 minutes
- **Standard Deviation:** 0.452 minutes
- **Coefficient of Variation:** 6.32%

### Bank of Providence (Individual Lines)
- **Mean:** 7.15 minutes
- **Standard Deviation:** 1.728 minutes
- **Coefficient of Variation:** 24.17%

### Comparison:
- **True or False:** Waiting times of customers at the Jefferson Valley Bank have more variation than the waiting times at the Bank of Providence.  
  **Answer:** False. The coefficient of variation is much higher for the Bank of Providence, indicating more variability in waiting times there.

- **True or False:** There is an obvious time saving when using a multiple line compared to using a single line for your clients at the bank.  
  **Answer:** False. The mean waiting times are the same, but the variability is higher for the multiple line system at the Bank of Providence.

Would you like to dive deeper into any part of this analysis or explore related concepts?

Here are 5 related questions:
1. How does the coefficient of variation help in comparing data sets with different units?
2. What does a higher coefficient of variation imply about a data set?
3. Can the coefficient of variation be used to compare data sets with different means?
4. How would these results change if we considered a different sample size or data set?
5. What are some potential factors that could contribute to the higher variation at the Bank of Providence?

**Tip:** Always compare coefficients of variation rather than just standard deviations when the means of two data sets are equal or similar.

Learn how to compare coefficients of variation for waiting times at Jefferson Valley Bank and Bank of Providence. Includes mean, standard deviation, and coefficient of variation calculations.

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