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.