Data set:
 5,5,14,10,25,4,5,3,7,4,13,10,5 ,3 ,6 ,4,6,7,5,8,8,6 ,6. Upper and lower outlier boundaries?

To find the upper and lower outlier boundaries for a data set, we can use the Interquartile Range (IQR) method. Here’s how you can do it:

### Step 1: Arrange the Data in Ascending Order
First, let's arrange the data in ascending order:

\[ 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 10, 10, 13, 14, 25 \]

### Step 2: Find the Quartiles (Q1, Q3)
- **Q1 (First Quartile)**: This is the median of the lower half of the data. For this data set, the lower half consists of the first 11 numbers: 
\[ 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6 \]
  The median (Q1) is 5.

- **Q3 (Third Quartile)**: This is the median of the upper half of the data. The upper half consists of the last 11 numbers:
\[ 6, 6, 6, 7, 7, 8, 8, 10, 10, 13, 14 \]
  The median (Q3) is 8.

### Step 3: Calculate the Interquartile Range (IQR)
\[ \text{IQR} = Q3 - Q1 = 8 - 5 = 3 \]

### Step 4: Calculate the Outlier Boundaries
- **Lower Bound**: \( Q1 - 1.5 \times \text{IQR} \)
\[ 5 - 1.5 \times 3 = 5 - 4.5 = 0.5 \]

- **Upper Bound**: \( Q3 + 1.5 \times \text{IQR} \)
\[ 8 + 1.5 \times 3 = 8 + 4.5 = 12.5 \]

### Step 5: Identify Outliers
- **Lower Outlier Boundary**: 0.5
- **Upper Outlier Boundary**: 12.5

Any data points below 0.5 or above 12.5 are considered outliers.

### Outliers in the Data Set
- Values above 12.5: 14, 25
- Values below 0.5: None

### Final Answer
- **Lower Outlier Boundary**: 0.5
- **Upper Outlier Boundary**: 12.5

Would you like to go into more detail or have any questions?

Here are five related questions you might consider:
1. How do you calculate the median for an odd-sized data set?
2. What happens if the data set has no outliers?
3. Can outliers significantly affect the mean and standard deviation of a data set?
4. What are the differences between the IQR method and the Z-score method for detecting outliers?
5. How would you handle outliers in a data set for statistical analysis?

**Tip:** Outliers can often provide valuable insights into the variability or anomalies in your data, so don't always discard them without considering their significance.

Data set: 5,5,14,10,25,4,5,3,7,4,13,10,5,3,6,4,6,7,5,8,8,6,6. Upper and lower outlier boundaries?

Find the upper and lower outlier boundaries for the data set 5,5,14,10,25,4,... using the Interquartile Range (IQR) method. Learn step-by-step how to calculate Q1, Q3, and identify outliers. Suitable for students in Grades 9-11.

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