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Let's analyze the data set you provided:  
\[ 24, 35, 36, 39, 40, 55, 55 \]

We need to find three values: the **lower quartile (Q1)**, the **median (Q2)**, and the **upper quartile (Q3)**. I'll break down each step:

1. **Median (Q2)**:
   The median is the middle value of the ordered data set. Since there are 7 values in this data set, the 4th value is the median.
   - Median = 39

2. **Lower Quartile (Q1)**:
   The lower quartile is the median of the lower half of the data, excluding the median itself. The lower half is \[24, 35, 36\]. The median of this subset is the 2nd value.
   - Lower quartile (Q1) = 35

3. **Upper Quartile (Q3)**:
   The upper quartile is the median of the upper half of the data, excluding the median itself. The upper half is \[40, 55, 55\]. The median of this subset is the 2nd value.
   - Upper quartile (Q3) = 55

### Final values:
- Lower quartile (Q1) = 35
- Median (Q2) = 39
- Upper quartile (Q3) = 55

Would you like more details or have any questions?

Here are 5 related questions to extend this:
1. How do you calculate the interquartile range (IQR) for this data set?
2. What is the range of this data set?
3. How do outliers relate to the quartiles in a data set?
4. How would the quartiles change if an additional value were added?
5. What is the significance of the quartiles in understanding data distribution?

**Tip:** Quartiles are useful in understanding the spread of the data, especially in identifying the middle 50% and detecting outliers.

In the data set below, what are the lower quartile, the median, and the upper quartile?

Data set: [24, 35, 36, 39, 40, 55, 55]

Learn how to find the lower quartile, median, and upper quartile for the data set [24, 35, 36, 39, 40, 55, 55]. Detailed steps are provided to help understand key concepts of statistics, including quartile theorem and median calculation. Suitable for Grades 6-8.

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