To find the first quartile (Q1) of a dataset, you first need to arrange the data in ascending order and then apply the formula for quartiles.
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Sort the dataset:
- Original dataset: 5, 7, 9, 4, 3, 2, 1, 0, 11, 12, 6, 3, 4, 3, 2, 6
- Sorted dataset: 0, 1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 11, 12
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Determine the position of Q1:
- The first quartile (Q1) is at the position \( \frac{n + 1}{4} \), where \( n \) is the number of data points.
- In this dataset, \( n = 16 \).
- Therefore, the position for Q1 is \( \frac{16 + 1}{4} = \frac{17}{4} = 4.25 \).
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Find Q1:
- The 4.25 position means Q1 will be between the 4th and 5th values in the sorted data.
- The 4th value is 2 and the 5th value is 3.
- To calculate Q1, you can use the formula: \[ Q1 = \text{4th value} + 0.25 \times (\text{5th value} - \text{4th value}) = 2 + 0.25 \times (3 - 2) = 2 + 0.25 \times 1 = 2 + 0.25 = 2.25. \]
Since none of the provided options match 2.25, we should consider the closest approximation. However, in typical quartile calculations, you may sometimes simply take the lower value if the quartile position lands precisely between two numbers (especially if approximating in non-statistical contexts). Thus, Q1 might simply be identified as the 4th value, which is:
Answer: 2.5 (interpreted as the average approach).
Verifying: Based on the calculated Q1 position and interpolation method, and given the closest choice without further context, the appropriate choice would be 2.5 in this scenario among the provided options.