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Part 1

Waiting times​ (in minutes) of customers in 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 mean and median for each of the two​ samples, then compare the two sets of results.

Single Line

6.56.5

6.66.6

6.76.7

6.86.8

7.07.0

7.17.1

7.47.4

7.87.8

7.87.8

7.87.8
 
Individual Lines

4.24.2

5.35.3

6.06.0

6.26.2

6.36.3

7.87.8

7.87.8

8.58.5

9.39.3

10.110.1

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Part 1

The mean waiting time for customers in a single line is 

7.157.15 

minutes.

Part 2

The median waiting time for customers in a single line is 

7.057.05 

minutes.

Part 3

The mean waiting time for customers in individual lines is 

enter your response here 

minutes.

Let's calculate the mean and median for the waiting times of customers in individual lines.

### Individual Lines Data:
4.2, 5.3, 6.0, 6.2, 6.3, 7.8, 7.8, 8.5, 9.3, 10.1

#### Step 1: Calculate the Mean
The mean is calculated by summing all the values and dividing by the number of values.

\[
\text{Mean} = \frac{\sum \text{Individual Lines}}{\text{Number of Values}}
\]

\[
\text{Mean} = \frac{4.2 + 5.3 + 6.0 + 6.2 + 6.3 + 7.8 + 7.8 + 8.5 + 9.3 + 10.1}{10}
\]

Let's calculate this:

\[
\text{Mean} = \frac{71.5}{10} = 7.15 \text{ minutes}
\]

### Step 2: Calculate the Median
To find the median, the data must be arranged in ascending order (which it already is). Since there are 10 values, the median will be the average of the 5th and 6th values.

The 5th value is 6.3 and the 6th value is 7.8.

\[
\text{Median} = \frac{6.3 + 7.8}{2} = \frac{14.1}{2} = 7.05 \text{ minutes}
\]

### Summary of Results
- **Mean waiting time for customers in individual lines:** 7.15 minutes
- **Median waiting time for customers in individual lines:** 7.05 minutes

These results indicate that the mean and median waiting times are exactly the same as in the single line scenario, meaning that the overall waiting times are quite similar between the two setups.

---

Do you have any questions or need further details? Here are five related questions:

1. How would the standard deviation compare between the two sets of data?
2. What does the similarity in mean and median suggest about the distribution of waiting times?
3. How would you calculate the range of waiting times for both setups?
4. If another customer were to join either line, how might that impact the mean?
5. How could the mode be useful in analyzing these waiting times?

**Tip:** The median is often a better measure of central tendency than the mean when dealing with skewed distributions.

Waiting times (in minutes) of customers in 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 mean and median for each of the two samples, then compare the two sets of results.

Learn how to calculate the mean and median waiting times for bank customers in a single line and individual lines. This statistical problem covers essential concepts such as mean, median, and comparing data sets. Suitable for high school students in Grades 9-12.

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