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To calculate the outlier limits of the given distribution, we typically follow these steps:

1. **Arrange the data**: Collect all the numbers in a single list.
2. **Calculate the quartiles**:
   - \( Q_1 \): The first quartile (25th percentile).
   - \( Q_3 \): The third quartile (75th percentile).
3. **Interquartile Range (IQR)**: \( IQR = Q_3 - Q_1 \).
4. **Outlier Limits**:
   - Lower limit: \( Q_1 - 1.5 \times IQR \).
   - Upper limit: \( Q_3 + 1.5 \times IQR \).

### Step 1: Collect the data
From the table:
\[ 30, 20, 10, 40, 25, 20, 10, 60, 15, 40, 5, 30, 12, 10, 10 \]

### Step 2: Sort the data
Sorted dataTo calculate the outlier limits of the given distribution, we typically follow these steps:

1. **Arrange the data**: Collect all the numbers in a single list.
2. **Calculate the quartiles**:
   - \( Q_1 \): The first quartile (25th percentile).
   - \( Q_3 \): The third quartile (75th percentile).
3. **Interquartile Range (IQR)**: \( IQR = Q_3 - Q_1 \).
4. **Outlier Limits**:
   - Lower limit: \( Q_1 - 1.5 \times IQR \).
   - Upper limit: \( Q_3 + 1.5 \times IQR \).

### Step 1: Collect the data
From the table:
\[ 30, 20, 10, 40, 25, 20, 10, 60, 15, 40, 5, 30, 12, 10, 10 \]

### Step 2: Sort the data
Sorted  
\[ 5, 10, 10, 10, 10, 12, 15, 20, 20, 25, 30, 30, 40, 40, 60 \]

### Step 3: Calculate the quartiles
- **Q1** (25th percentile): The 1st quartile is the 4th value (since there are 15 values): \( Q_1 = 10 \).
- **Q3** (75th percentile): The 3rd quartile is the 12th value: \( Q_3 = 30 \).

### Step 4: Calculate the IQR
\[ IQR = Q_3 - Q_1 = 30 - 10 = 20 \]

### Step 5: Calculate the outlier limits
- **Lower limit**: \( Q_1 - 1.5 \times IQR = 10 - 1.5 \times 20 = 10 - 30 = -20 \).
- **Upper limit**: \( Q_3 + 1.5 \times IQR = 30 + 1.5 \times 20 = 30 + 30 = 60 \).

### Conclusion
- The **lower limit** is \(-20\).
- The **upper limit** is \(60\).

Values outside of this range would be considered outliers.

Would you like more details on the process or any specific step?

### Related Questions:
1. How are quartiles different from percentiles in statistical analysis?
2. What is the significance of using 1.5 times the IQR to determine outliers?
3. Can the method for calculating outliers be applied to non-numerical data?
4. How do extreme outliers affect the mean and median of a dataset?
5. Is there an alternative method to identify outliers besides using the IQR?

### Tip:
When analyzing distributions, it's important to visualize the data (using a box plot, for example) to easily identify outliers and their impact on the overall dataset.

Calculate the outlier limits of the distribution. Write the lower and upper limits.

Learn how to calculate the outlier limits for a data distribution with step-by-step instructions. This example covers sorting the data, finding quartiles (Q1 and Q3), computing the IQR, and determining the upper and lower outlier boundaries. Suitable for high school statistics students.

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