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

$\text{Coefficient of Variation (CV)} = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\%$

Step 1: Calculate the mean and standard deviation for each bank.

Bank A (single line)

Data: $6.6, 6.6, 6.7, 6.8, 7.1, 7.2, 7.5, 7.6, 7.6, 7.7$

Bank B (individual lines)

Data: $4.3, 5.4, 5.9, 6.3, 6.8, 7.6, 7.7, 8.5, 9.4, 9.7$

I'll calculate the mean and standard deviation for each bank, then apply the formula to find the coefficient of variation for Bank B, rounded to one decimal place.import numpy as np

Data for Bank A and Bank B

bank_a = [6.6, 6.6, 6.7, 6.8, 7.1, 7.2, 7.5, 7.6, 7.6, 7.7] bank_b = [4.3, 5.4, 5.9, 6.3, 6.8, 7.6, 7.7, 8.5, 9.4, 9.7]

Calculating mean and standard deviation for Bank A

mean_a = np.mean(bank_a) std_dev_a = np.std(bank_a, ddof=1) # Sample standard deviation cv_a = (std_dev_a / mean_a) * 100

Calculating mean and standard deviation for Bank B

mean_b = np.mean(bank_b) std_dev_b = np.std(bank_b, ddof=1) # Sample standard deviation cv_b = (std_dev_b / mean_b) * 100

cv_a, cv_b(6.200544431702706, 24.406510608690137)(6.200544431702706, 24.406510608690137)successThe coefficient of variation (CV) for each bank is as follows:

• Bank A (single line): $6.2\%$
• Bank B (individual lines): $24.4\%$

Comparison

Bank B has a significantly higher coefficient of variation compared to Bank A, indicating that there is more relative variability in the waiting times for customers at Bank B (individual lines) than at Bank A (single line). This suggests that wait times are less consistent at Bank B.

Would you like further details on the calculation process, or have any questions?

Related Questions

1. What impact does a higher coefficient of variation have on customer satisfaction?
2. How can the coefficient of variation be reduced in a bank setting?
3. What other statistical measures could be useful to compare the two banks?
4. What assumptions are made when calculating the coefficient of variation?
5. How does the coefficient of variation differ from standard deviation in interpretation?

Tip: When comparing consistency between two data sets, the coefficient of variation is particularly helpful because it standardizes the measure of variability relative to the mean.