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The bar graph shows the results from 20 throws of a die, with the frequency of each score (from 1 to 6) displayed on the graph. To determine the lower quartile (Q1), we need to analyze the data and find the value below which 25% of the observations lie.

### Steps to Find the Lower Quartile:

1. **Total Observations:** There are 20 throws in total.

2. **Frequency Distribution:**
   - Score 1: 2 times
   - Score 2: 5 times
   - Score 3: 3 times
   - Score 4: 4 times
   - Score 5: 4 times
   - Score 6: 2 times

3. **Cumulative Frequency:**
   - Score 1: 2
   - Score 2: 7 (2 + 5)
   - Score 3: 10 (7 + 3)
   - Score 4: 14 (10 + 4)
   - Score 5: 18 (14 + 4)
   - Score 6: 20 (18 + 2)

4. **Finding the Lower Quartile:**
   - \( Q_1 \) is the value at the \( \frac{1}{4} \times 20 = 5^{th} \) observation.
   - According to the cumulative frequency, the 5th observation falls in the score of 2.

Thus, the lower quartile \( Q_1 \) is **2**.

### Answer:
**A. 2**

Would you like more details or have any questions?

Here are five related questions you might find useful:

1. How do you calculate the median and upper quartile from a data set?
2. What is the difference between a quartile and a percentile?
3. How does a box plot represent quartiles visually?
4. What are some common applications of quartiles in data analysis?
5. How do outliers affect the calculation of quartiles?

**Tip:** When calculating quartiles, always make sure to order your data from smallest to largest, as this will help you correctly identify the positions of the quartiles.

The bar graph shows the scores obtained from 20 throws of a die. What is the lower quartile?

Learn how to find the lower quartile (Q1) from a frequency distribution based on 20 throws of a die. Understand the concept of cumulative frequency and how it applies to determining quartiles. Suitable for students in Grades 6-8.

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