To calculate the five-number summary of the given data set \(11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25\), we first need to organize the data (which is already sorted) and then identify the minimum, maximum, and quartiles.
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Minimum value (Min): The smallest number in the data set. \[ \text{Min} = 11 \]
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Maximum value (Max): The largest number in the data set. \[ \text{Max} = 25 \]
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Median (Q2): The median is the middle value of the data set. Since there are 11 numbers (an odd count), the median is the 6th number. \[ \text{Median} = 13 \]
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Quartile 1 (Q1): This is the median of the first half of the data set (the lower half). The lower half is: \[ 11, 12, 12, 13, 13 \] The median of these numbers (the 3rd number in this set) is: \[ Q1 = 12 \]
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Quartile 3 (Q3): This is the median of the second half of the data set (the upper half). The upper half is: \[ 13, 14, 14, 15, 19, 25 \] The median of these numbers (the 3rd number in this set) is: \[ Q3 = 15 \]
Now, we can summarize the calculations for the five-number summary:
- Minimum: \(11\)
- Q1: \(12\)
- Median (Q2): \(13\)
- Q3: \(15\)
- Maximum: \(25\)
Thus, the five-number summary is:
- Min: \(11\)
- Q1: \(12\)
- Median: \(13\)
- Q3: \(15\)
- Max: \(25\)