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The question asks to determine the value of the first quartile from the given data set:

**Data set:** 3, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11.

### Steps to find the first quartile (Q1):

1. **Order the data**: The data is already sorted in ascending order.

2. **Find the first quartile (Q1)**:
   - Q1 is the value that represents the 25th percentile of the data.
   - To find the position of Q1, we use the formula:  
     \[
     Q1 = \frac{(n + 1)}{4}
     \]
     where \( n \) is the number of data points.

3. **Count the data points**: There are 21 data points.

   Using the formula for Q1:
   \[
   Q1 = \frac{(21 + 1)}{4} = \frac{22}{4} = 5.5
   \]

   This means the first quartile is between the 5th and 6th data points in the list. The 5th data point is **6**, and the 6th data point is also **6**.

### Conclusion:
The value of the first quartile (Q1) is **6**.

Would you like further details or have any questions?

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Here are 5 related questions you can explore:

1. How do you calculate the median (second quartile) for a data set?
2. What is the formula to find the third quartile (Q3)?
3. How is the interquartile range (IQR) calculated and what does it represent?
4. What is the significance of outliers when using quartiles?
5. How does the quartile method differ from calculating percentiles?

**Tip**: When dealing with quartiles, always ensure that the data is sorted before performing calculations.

A poll asks shoppers at the mall how many cups of water they typically drink in a day. The results of the poll are listed below: 3, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11. What is the value of the first quartile?

Learn how to calculate the first quartile (Q1) from a data set representing daily water consumption. The solution walks through identifying Q1 using the formula (n + 1) / 4. Data points include numbers ranging from 3 to 11.

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