(a) Determine and interpret the quartiles.

By the​ quartiles, about 

enter your response here​% 

of the wait times are 

Upper Q 1Q1equals=enter your response here 

​minute(s) or​ less, and about 

enter your response here​% 

of the wait times exceed 

Upper Q 1Q1 

​minute(s); about 

enter your response here​% 

of the wait times are 

Upper Q 2Q2equals=enter your response here 

​minute(s) or less and about 

enter your response here​% 

of the wait times exceed 

Upper Q 2Q2 

​minute(s); about 

enter your response here​% 

of the wait times are 

Upper Q 3Q3equals=enter your response here 

​minute(s) or​ less, and about 

enter your response here​% 

of the wait times exceed 

Upper Q 3Q3 

​minute(s).

​(Type integers or decimals. Do not​ round.)

Part 2

​(b) Does the data set have​ outliers? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The​ outlier(s) in the data set​ is(are) 

enter your response here.

​(Use a comma to separate answers as​ needed.)

B.

This data set does not have any outliers. 6

15

3

6

5

29

7

5

25

9

8

45

11

11

33

0

28

6

9

5

19

8

22

9

30

16

55

2

11

29

0

2

5

10

3

8

5

13

7

16

### Part 1: Quartile Calculation and Interpretation

We will first calculate the quartiles for the given dataset, and then interpret them according to the problem's structure.

The data set is:
\[
6, 15, 3, 6, 5, 29, 7, 5, 25, 9, 8, 45, 11, 11, 33, 0, 28, 6, 9, 5, 19, 8, 22, 9, 30, 16, 55, 2, 11, 29, 0, 2, 5, 10, 3, 8, 5, 13, 7, 16
\]

To find the quartiles, follow these steps:
1. **Arrange the data in increasing order**:
   \[
   0, 0, 2, 2, 3, 3, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 11, 11, 11, 11, 13, 15, 16, 16, 19, 22, 25, 28, 29, 29, 30, 33, 45, 55
   \]

2. **Number of data points**: There are 42 values.

3. **Quartiles**:
   - **First Quartile (Q1)**: The 25th percentile. This is at position \( \frac{42+1}{4} = 10.75 \). So, take the average of the 10th and 11th values: 
     \[
     Q1 = \frac{5 + 5}{2} = 5
     \]
   - **Second Quartile (Q2 or Median)**: The 50th percentile. This is at position \( \frac{42+1}{2} = 21.5 \). So, take the average of the 21st and 22nd values: 
     \[
     Q2 = \frac{9 + 9}{2} = 9
     \]
   - **Third Quartile (Q3)**: The 75th percentile. This is at position \( \frac{3(42+1)}{4} = 32.25 \). So, take the average of the 32nd and 33rd values: 
     \[
     Q3 = \frac{16 + 19}{2} = 17.5
     \]

4. **Interpretation**:
   - About **25%** of the wait times are **5 minutes or less**.
   - About **75%** of the wait times exceed **5 minutes**.
   - About **50%** of the wait times are **9 minutes or less**.
   - About **50%** of the wait times exceed **9 minutes**.
   - About **75%** of the wait times are **17.5 minutes or less**.
   - About **25%** of the wait times exceed **17.5 minutes**.

### Part 2: Outlier Detection

To detect outliers, we will use the **Interquartile Range (IQR)**:
\[
IQR = Q3 - Q1 = 17.5 - 5 = 12.5
\]
Now, calculate the boundaries for outliers:
- **Lower bound**: \( Q1 - 1.5 \times IQR = 5 - 1.5 \times 12.5 = 5 - 18.75 = -13.75 \) (no negative outliers since all data is non-negative).
- **Upper bound**: \( Q3 + 1.5 \times IQR = 17.5 + 1.5 \times 12.5 = 17.5 + 18.75 = 36.25 \).

Any data points greater than 36.25 are considered outliers. From the data set, the outliers are:
\[
45, 55
\]

### Conclusion for Part 2:
The outliers in the data set are **45** and **55**.

---

Would you like more details or further clarifications? Here are some related questions to deepen your understanding:

1. How would you calculate the quartiles for a different dataset?
2. Why is the Interquartile Range (IQR) used for detecting outliers?
3. Can a dataset have more than two outliers? How would you handle such a case?
4. How do quartiles help in understanding the spread of data?
5. How does changing the dataset affect the calculation of quartiles and outliers?

**Tip**: Always double-check data order when calculating quartiles; an incorrect order can lead to errors in your calculations.

Determine and interpret the quartiles for the given dataset, and check if there are any outliers.

Learn how to calculate and interpret the quartiles (Q1, Q2, Q3) for a dataset and detect outliers using the interquartile range (IQR). This solution covers the dataset: 6, 15, 3, 6, 5, 29, 7, 5, 25, 9, 8, 45, 11, 11, 33, 0, 28, 6, 9, 5, 19, 8, 22, 9, 30, 16, 55, 2, 11, 29, 0, 2, 5, 10, 3, 8, 5, 13, 7, 16. Suitable for high school students.

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