To find the 5-number summary of the dataset \(5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16\), we first need to determine the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
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Minimum: The smallest number in the dataset is 5.
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Maximum: The largest number in the dataset is 16.
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Median (Q2): Since there are 12 data points (an even number), the median is the average of the 6th and 7th values in the ordered dataset. \[ \text{Median} = \frac{8 + 8}{2} = 8 \]
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First Quartile (Q1): Q1 is the median of the first half of the data (the first 6 values: 5, 6, 6, 7, 7, 8). Again, since there are 6 numbers, the median is the average of the 3rd and 4th values. \[ Q1 = \frac{6 + 7}{2} = 6.5 \]
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Third Quartile (Q3): Q3 is the median of the second half of the data (the last 6 values: 8, 8, 9, 9, 14, 16). We find the median of these 6 numbers, which is the average of the 3rd and 4th values. \[ Q3 = \frac{9 + 9}{2} = 9 \]
The 5-number summary is:
- Minimum: 5
- Q1: 6.5
- Median (Q2): 8
- Q3: 9
- Maximum: 16
From the provided choices, the value for quartile 3 (Q3) is:
- 9.