To identify the first quartile (Q1) of the dataset, we first need to organize the data in ascending order.
The given dataset is: 5, 7, 9, 4, 3, 2, 1, 0, 11, 12, 6, 3, 4, 3, 2, 6
Now, let's sort this data in ascending order: 0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 11, 12
Next, we need to find the first quartile (Q1). The first quartile is the value that separates the lowest 25% of the data from the rest.
To find Q1:
- Count the number of data points. There are 16 data points.
- To find Q1, we will calculate the position using the formula: \[ Q1 = \frac{(n + 1)}{4} \] where \( n \) is the number of data points. \[ Q1 = \frac{(16 + 1)}{4} = \frac{17}{4} = 4.25 \]
This means that Q1 is located between the 4th and 5th sorted values.
The 4th value is 2, and the 5th value is 3. To find Q1, we will take the average of these two values:
\[ Q1 = \frac{2 + 3}{2} = \frac{5}{2} = 2.5 \]
Thus, the first quartile (Q1) in the dataset is \( 2.5 \).
The correct response is: 2.5