Question

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Measures of Variation Quick Check
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Question
Identify the first quartile in the following dataset:
5, 7, 9, 4, 3, 2, 1, 0, 11, 12, 6, 3, 4, 3, 2, 6(1 point)
Responses

0
0

4
4

2.5
2.5

6.5
6.5
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Answer 1

To find the first quartile (Q1) of the dataset, we need to follow these steps:

1. **Arrange the data in ascending order**:
The dataset is: 5, 7, 9, 4, 3, 2, 1, 0, 11, 12, 6, 3, 4, 3, 2, 6.
Arranged in order: **0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 11, 12**.

2. **Determine the position of the first quartile (Q1)**:
The first quartile is the value at the position \( \frac{n + 1}{4} \) where \( n \) is the number of data points.
Here, \( n = 16 \) (since there are 16 numbers).

\[
\text{Position of Q1} = \frac{16 + 1}{4} = \frac{17}{4} = 4.25
\]

This means Q1 is located between the 4th and 5th values in the ordered dataset.

3. **Locate the 4th and 5th values**:
From the ordered dataset:
- 4th value = 2
- 5th value = 3

4. **Calculate Q1**:
Since Q1 is halfway between the 4th and 5th values:
\[
Q1 = \frac{2 + 3}{2} = \frac{5}{2} = 2.5
\]

Thus, the first quartile (Q1) is **2.5**.

### **Final Answer: 2.5**