Obtain Q1 for these data (sample of 12) : 
 35  29  44  72  34  64  41  50  54  104  39  58 


To find \( Q_1 \) (the first quartile), we must follow these steps:

### Step 1: Arrange the data in ascending order
The given data set is:
\[ 35, 29, 44, 72, 34, 64, 41, 50, 54, 104, 39, 58 \]

Arranging in ascending order:
\[ 29, 34, 35, 39, 41, 44, 50, 54, 58, 64, 72, 104 \]

### Step 2: Find the position of \( Q_1 \)
For a sample of size \( n = 12 \), the first quartile \( Q_1 \) is the median of the lower half of the data.

The lower half includes the first 6 data points:
\[ 29, 34, 35, 39, 41, 44 \]

The median of this subset is the average of the 3rd and 4th values (since \( n = 6 \), an even number):
\[
Q_1 = \frac{35 + 39}{2} = \frac{74}{2} = 37
\]

### Answer:
The first quartile \( Q_1 \) is **37**.

Would you like further details or have any questions?

Here are some related questions to explore:
1. How do you find \( Q_3 \) from the same dataset?
2. How does the interquartile range (IQR) relate to the quartiles?
3. Can \( Q_1 \) be calculated using an alternative method?
4. What is the importance of quartiles in statistical analysis?
5. How would you interpret \( Q_1 \) in this context?

**Tip:** Quartiles are useful for identifying the spread and skewness of the data, with \( Q_1 \) representing the 25th percentile.

Obtain Q1 for these data (sample of 12) : 35  29  44  72  34  64  41  50  54  104  39  58

Learn how to calculate the first quartile (Q1) for a data sample of 12 values: 35, 29, 44, 72, 34, 64, 41, 50, 54, 104, 39, 58. This step-by-step guide walks through arranging data, finding Q1, and understanding its significance. Perfect for students in Grades 7-10.

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