To find the lower quartile (Q1), median (Q2), and upper quartile (Q3) in the provided data set \(30, 33, 66, 67, 73, 73, 82\), we first need to arrange the data in ascending order, which it already is.
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Lower Quartile (Q1): This is the median of the lower half of the data (excluding the overall median if there is an odd number of observations).
- The lower half of the data is \(30, 33, 66\).
- To find Q1, find the median of \(30, 33, 66\):
- Median = \(33\).
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Median (Q2): This is the middle value of the data set.
- Since there are 7 data points, the median is the 4th value:
- Median = \(67\).
- Since there are 7 data points, the median is the 4th value:
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Upper Quartile (Q3): This is the median of the upper half of the data (excluding the overall median if there is an odd number of observations).
- The upper half of the data is \(67, 73, 73, 82\).
- To find Q3, find the median of \(73, 73, 82\):
- Median = \(73\).
Now we can summarize the results:
- Lower quartile (Q1) = \(66\)
- Median (Q2) = \(67\)
- Upper quartile (Q3) = \(73\)
Therefore:
- Lower quartile = 66
- Median = 67
- Upper quartile = 73