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To find the coefficient of variation (CV) for the waiting times at Bank A, we will use the following steps:

### Formula:
\[
\text{CV} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100
\]

#### Steps:
1. **Calculate the mean** of the waiting times for Bank A.
2. **Calculate the standard deviation** of the waiting times for Bank A.
3. Use the formula to compute the coefficient of variation.

### Bank A Waiting Times:
\[
6.5, 6.6, 6.7, 6.8, 7.0, 7.3, 7.5, 7.6, 7.6, 7.7
\]

#### 1. Calculate the Mean:
\[
\text{Mean} = \frac{6.5 + 6.6 + 6.7 + 6.8 + 7.0 + 7.3 + 7.5 + 7.6 + 7.6 + 7.7}{10}
\]
\[
\text{Mean} = \frac{70.3}{10} = 7.03
\]

#### 2. Calculate the Standard Deviation:
We will use the formula for the sample standard deviation:
\[
\text{SD} = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}}
\]
Where \( x_i \) are the individual waiting times, \( \mu \) is the mean, and \( n \) is the number of data points.

- \( (6.5 - 7.03)^2 = 0.2809 \)
- \( (6.6 - 7.03)^2 = 0.1849 \)
- \( (6.7 - 7.03)^2 = 0.1089 \)
- \( (6.8 - 7.03)^2 = 0.0529 \)
- \( (7.0 - 7.03)^2 = 0.0009 \)
- \( (7.3 - 7.03)^2 = 0.0729 \)
- \( (7.5 - 7.03)^2 = 0.2209 \)
- \( (7.6 - 7.03)^2 = 0.3249 \)
- \( (7.6 - 7.03)^2 = 0.3249 \)
- \( (7.7 - 7.03)^2 = 0.4489 \)

Sum of squared differences: \( 0.2809 + 0.1849 + 0.1089 + 0.0529 + 0.0009 + 0.0729 + 0.2209 + 0.3249 + 0.3249 + 0.4489 = 2.020 \)

Now divide by \( n - 1 = 10 - 1 = 9 \):
\[
\frac{2.020}{9} = 0.2244
\]

Take the square root to find the standard deviation:
\[
\text{SD} = \sqrt{0.2244} \approx 0.474
\]

#### 3. Calculate the Coefficient of Variation:
\[
\text{CV} = \left( \frac{0.474}{7.03} \right) \times 100 \approx 6.7\%
\]

### Final Answer:
The coefficient of variation for the waiting times at Bank A is approximately **6.7%**.

Would you like further clarification or more details?

### 5 Related Questions:
1. How is the coefficient of variation interpreted in statistics?
2. What are some real-life scenarios where CV is useful?
3. How does the CV of Bank A compare to Bank B's variation?
4. How do you calculate standard deviation for larger datasets quickly?
5. Why is it important to use \( n-1 \) (Bessel's correction) when calculating sample standard deviation?

**Tip:** The coefficient of variation is useful for comparing the variability between datasets with different units or means.

Find the coefficient of variation for the waiting times at Bank A (single line) with the following data points: 6.5, 6.6, 6.7, 6.8, 7.0, 7.3, 7.5, 7.6, 7.6, 7.7.

Learn how to calculate the coefficient of variation for Bank A's waiting times, including calculating the mean and sample standard deviation. This statistical problem uses data points like 6.5, 6.6, 6.7, 6.8, 7.0, 7.3, 7.5, 7.6, 7.6, and 7.7 to find the CV.

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