To calculate the 5-number summary (minimum, Quartile 1 (Q1), median, Quartile 3 (Q3), and maximum) for the dataset \( 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25 \), we can follow these steps:
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Minimum Value: The smallest value in the dataset.
- Minimum = 11
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Maximum Value: The largest value in the dataset.
- Maximum = 25
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Median: The median is the middle value when the data is sorted. Since there are 11 data points (an odd number), the median will be the 6th value.
- The sorted dataset is already in order: \( 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25 \)
- Median = 13 (the 6th value)
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Quartile 1 (Q1): Q1 is the median of the first half of the dataset (the lower half). This includes the first 5 data points.
- First half: \( 11, 12, 12, 13, 13 \)
- Median of the first half (5 data points): the 3rd value, which is 12.
- Q1 = 12
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Quartile 3 (Q3): Q3 is the median of the second half of the dataset (the upper half). This includes the last 5 data points.
- Second half: \( 13, 14, 14, 15, 19, 25 \)
- Median of the second half (5 data points): the 8th value from the sorted dataset which is 14.
- Q3 = 19
Now, compiling all values:
- Minimum = 11
- Q1 = 12
- Median = 13
- Q3 = 19
- Maximum = 25
Final 5-number summary:
- Minimum: 11
- Q1: 12
- Median: 13
- Q3: 19
- Maximum: 25