To solve for the first and third quartiles of the given data set, let's first organize the numbers in ascending order and then calculate the quartiles.

Given Data:

4, 10, 6, 3, 13, 4, 5, 5, 6, 6, 10, 3, 8, 5, 26, 4, 11, 3, 5, 7, 8, 3, 6, 3

Step 1: Sort the Data

Sorting these values in ascending order gives:

3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 10, 10, 11, 13, 26

Step 2: Find the Quartiles

• First Quartile (Q1): This is the median of the lower half of the data. The lower half of the data set is:

3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5

The median of this half (average of the 6th and 7th values): $Q1 = \frac{4 + 4}{2} = 4$

• Third Quartile (Q3): This is the median of the upper half of the data. The upper half of the data set is:

6, 6, 6, 6, 7, 8, 8, 10, 10, 11, 13, 26

The median of this half (average of the 6th and 7th values): $Q3 = \frac{8 + 8}{2} = 8$

Final Answer:

• First Quartile (Q1) = 4
• Third Quartile (Q3) = 8

Would you like more details on this solution or have any further questions?

Here are 5 related questions:

1. How do you find the interquartile range (IQR) using Q1 and Q3?
2. Can you explain how to calculate the median for an odd set of data?
3. What is the difference between a quartile and a percentile?
4. How would you interpret a box plot that uses quartiles?
5. How can outliers affect the quartiles in a data set?

Tip: When finding quartiles, always ensure the data is sorted first!