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Let's work through the data to find the quartiles. The data set given is:

**59, 63, 62, 65, 56, 61, 54, 63, 55, 59, 58, 57, 56, 58, 80**

### Step 1: Organize the Data
First, we need to arrange the data in ascending order:

**54, 55, 56, 56, 57, 58, 58, 59, 59, 61, 62, 63, 63, 65, 80**

### Step 2: Calculate the Quartiles
Quartiles divide the data into four parts. We will calculate the 1st quartile (Q1), 2nd quartile (Q2 or the median), and the 3rd quartile (Q3).

- **Q1** (the 1st quartile): The median of the lower half of the data.
- **Q2** (the 2nd quartile or median): The median of the entire data set.
- **Q3** (the 3rd quartile): The median of the upper half of the data.

#### Median (Q2):
The total number of values is 15, so the median is the 8th value in the ordered data.

**Q2 = 59**

#### 1st Quartile (Q1):
The lower half of the data (excluding the median) is:

**54, 55, 56, 56, 57, 58, 58**

The median of this lower half is the 4th value:

**Q1 = 56**

#### 3rd Quartile (Q3):
The upper half of the data (excluding the median) is:

**59, 61, 62, 63, 63, 65, 80**

The median of this upper half is the 4th value:

**Q3 = 63**

### Step 3: Summary of Quartiles
- **Q1 = 56**
- **Q2 = 59**
- **Q3 = 63**

Would you like further details or clarification on any part of this? 

### Related Questions:
1. What is the interquartile range (IQR) of the data set?
2. How do you calculate the median of a data set?
3. What are the steps to find outliers in a data set?
4. What is the significance of quartiles in data analysis?
5. How do you interpret the spread of data using quartiles?

### Tip:
When calculating quartiles, it helps to split the data set into lower and upper halves carefully, especially when the total number of observations is odd.

Use the accompanying data set to find the quartiles, the interquartile range, and identify any outliers. Data set: 59, 63, 62, 65, 56, 61, 54, 63, 55, 59, 58, 57, 56, 58, 80

This problem involves finding the first quartile, second quartile (median), and third quartile for a data set, along with calculating the interquartile range and identifying any outliers. The data set consists of the following values: 59, 63, 62, 65, 56, 61, 54, 63, 55, 59, 58, 57, 56, 58, and 80.

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