To calculate the 5-number summary of the given dataset, we need to identify the following five values: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
The dataset is: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16
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Minimum: The smallest value in the dataset.
- Minimum = 5
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Maximum: The largest value in the dataset.
- Maximum = 16
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Median (Q2): The middle value when the data is arranged in order. Since there are 12 numbers (an even number), the median will be the average of the two middle numbers.
- The two middle numbers are the 6th and 7th values in the ordered list: 8 and 8.
- Median (Q2) = (8 + 8) / 2 = 8
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First Quartile (Q1): The median of the first half of the data. The first half consists of the first 6 values: 5, 6, 6, 7, 7, 8.
- The median of this subset is the average of the 3rd and 4th values (6 and 7).
- Q1 = (6 + 7) / 2 = 6.5
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Third Quartile (Q3): The median of the second half of the data. The second half consists of the last 6 values: 8, 9, 9, 14, 16.
- The median of this subset is the average of the 3rd and 4th values (9 and 14).
- Q3 = (9 + 14) / 2 = 11.5
Putting it all together, the 5-number summary is:
- Minimum = 5
- Q1 = 6.5
- Median (Q2) = 8
- Q3 = 11.5
- Maximum = 16
5-number summary: (5, 6.5, 8, 11.5, 16)