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Part 1
Find the mean and median for the waiting times at Big Bank given below. Show your work​ clearly, and verify that both are the same. The following values are measured in minutes.
Big Bank​ (three lines): 4.1  5.2  5.6  6.2  6.7  7.2  7.7  7.7  8.5  9.3  11.0
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Part 1
Which of the following shows how to compute the​ mean?
A.
meanequals​(sum of all ​values)times​(total number of​ values)
B.
meanequalssum of all valuesplustotal number of values
C.
meanequalsStartFraction sum of all values Over total number of values EndFraction
Your answer is correct.D.
meanequalsStartFraction total number of values Over sum of all values EndFraction
Part 2
The sum of all values is 
  
enter your response here.
​(Type an integer or a​ decimal.)

Let's go step by step to calculate both the **mean** and **median** for the waiting times at Big Bank and verify that they are indeed the same.

### Given Data:
The waiting times (in minutes) are:
\[ 4.1, 5.2, 5.6, 6.2, 6.7, 7.2, 7.7, 7.7, 8.5, 9.3, 11.0 \]

#### **Part 1: Calculating the Mean**

The formula for the mean is:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}
\]

Step 1: Find the sum of all the values.

\[
\text{Sum} = 4.1 + 5.2 + 5.6 + 6.2 + 6.7 + 7.2 + 7.7 + 7.7 + 8.5 + 9.3 + 11.0 = 78.2
\]

Step 2: Count the total number of values.

There are **11** waiting times.

Step 3: Compute the mean.

\[
\text{Mean} = \frac{78.2}{11} \approx 7.11 \text{ minutes}
\]

#### **Part 2: Calculating the Median**

The median is the middle value when the data is arranged in increasing order.

Step 1: Arrange the values in increasing order (already done):
\[
4.1, 5.2, 5.6, 6.2, 6.7, 7.2, 7.7, 7.7, 8.5, 9.3, 11.0
\]

Step 2: Since there are 11 values (an odd number), the median is the middle value, which is the 6th value in the ordered list:
\[
\text{Median} = 7.2 \text{ minutes}
\]

#### **Verification: Are the Mean and Median the Same?**

- **Mean**: \( 7.11 \) minutes
- **Median**: \( 7.2 \) minutes

As we can see, **the mean and median are close but not exactly the same**. The mean is approximately 7.11, while the median is exactly 7.2. Therefore, they are not the same, even though they are very close.

#### **Answer to Multiple Choice:**
The correct formula to compute the mean is:
\[
\boxed{C. \, \text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}}
\]

#### **Part 2: The sum of all values**
The sum of the values is:
\[
\boxed{78.2}
\]

---

Do you want more details or have any questions?

### Related Questions:
1. What would happen if we added more values to this data set? How would it affect the mean and median?
2. Why is the mean slightly less than the median in this data set?
3. How would we calculate the mode for this data set? What is it?
4. If one more value was added to the list, making the number of data points even, how would you calculate the median?
5. How do outliers affect the mean compared to the median?

**Tip:** The mean is sensitive to outliers, while the median gives a better sense of the central tendency in skewed data.

Find the mean and median for the waiting times at Big Bank given below. Show your work clearly, and verify that both are the same. The following values are measured in minutes: 4.1, 5.2, 5.6, 6.2, 6.7, 7.2, 7.7, 7.7, 8.5, 9.3, 11.0

Learn how to calculate the mean and median of Big Bank's waiting times with a step-by-step guide. This problem covers essential statistical concepts, including how to find the mean by summing the values and dividing by the total number of data points, and how to find the median by identifying the middle value in an ordered data set. Suitable for Grades 6-8.

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