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Let's first analyze the table you provided. We are tasked with determining the **1st quartile (Q1)**, **2nd quartile (Q2 or Median)**, and **3rd quartile (Q3)**.

### Data Analysis:
The total number of students (data points) is 20, as shown by the cumulative frequency. Here's how we find the quartiles:

#### 1. **2nd Quartile (Median, Q2)**:
To find the median, we locate the middle position:
- Position of the median = \( \frac{n + 1}{2} = \frac{20 + 1}{2} = 10.5 \)

The 10.5th data point lies between the 10th and 11th positions.
From the cumulative frequency table:
- The 10th and 11th data points are in the group where # of siblings = 2 (Cumulative Frequency = 12), so **Median (Q2) = 2**.

#### 2. **1st Quartile (Q1)**:
The 1st quartile is at the 25th percentile:
- Position of Q1 = \( \frac{n + 1}{4} = \frac{20 + 1}{4} = 5.25 \)

The 5.25th data point lies in the group where # of siblings = 1 (Cumulative Frequency = 7), so **Q1 = 1**.

#### 3. **3rd Quartile (Q3)**:
The 3rd quartile is at the 75th percentile:
- Position of Q3 = \( \frac{3(n + 1)}{4} = \frac{3(20 + 1)}{4} = 15.75 \)

The 15.75th data point lies in the group where # of siblings = 3 (Cumulative Frequency = 16), so **Q3 = 3**.

### Summary of Results:
- **Q1 (1st Quartile)** = 1
- **Q2 (Median)** = 2
- **Q3 (3rd Quartile)** = 3

Would you like details on how to calculate the range or other aspects of this dataset?

### Follow-up Questions:
1. How would you calculate the interquartile range (IQR) using Q1 and Q3?
2. Can you determine the mode from the table? What is it?
3. How would the results change if there were an additional data point?
4. What does the range of this dataset tell you about the distribution of siblings?
5. How would you create a box plot using the quartile values?

**Tip**: The interquartile range (IQR) is a good measure of spread that is less affected by extreme values than the range.

Determine the Median (2nd Quartile), First Quartile, Third Quartile, and Range based on the frequency table showing the number of siblings for 20 students.

Learn how to calculate the median (Q2), first quartile (Q1), third quartile (Q3), and range using a frequency table. This problem shows the distribution of siblings among 20 students. A perfect resource for Grades 9-12 statistics lessons.

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