Let's find the lower quartile, median, and upper quartile of the data set:

The data set is: $5, 6, 6, 8, 8, 9$.

Step 1: Median (Q2)

• To find the median, arrange the data in order (already done).
• Since the number of data points is 6 (even), the median is the average of the 3rd and 4th values.
• The 3rd and 4th values are $6$ and $8$. $\text{Median} = \frac{6 + 8}{2} = 7$

Step 2: Lower Quartile (Q1)

• The lower quartile is the median of the lower half of the data, excluding the overall median. The lower half is $5, 6, 6$.
• The median of this subset is the 2nd value, which is $6$.

Step 3: Upper Quartile (Q3)

• The upper quartile is the median of the upper half of the data, excluding the overall median. The upper half is $8, 8, 9$.
• The median of this subset is the 2nd value, which is $8$.

Summary:

• Lower quartile (Q1) = 6
• Median (Q2) = 7
• Upper quartile (Q3) = 8

Would you like more details or further clarification?

Here are five related questions for practice:

1. What are the quartiles of the data set $3, 5, 7, 8, 9, 10, 12$?
2. How do you calculate quartiles for a data set with an odd number of values?
3. What is the interquartile range (IQR) for this data set?
4. Why is it important to exclude the median when calculating Q1 and Q3?
5. How would the quartiles change if the number 10 was added to this data set?

Tip: Quartiles divide your data into four equal parts, helping identify the spread and center of the data.