To find the lower quartile (Q1), median (Q2), and upper quartile (Q3) of the data set, we first need to organize the numbers in ascending order. The given data is:
73529476221522123420
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Sort the numbers in ascending order:
- The sorted order is: 2, 2, 2, 2, 3, 4, 5, 6, 7, 7, 7, 8, 9
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Determine the quartiles:
- The sorted data set consists of 20 numbers.
\[ [2, 2, 2, 2, 3, 4, 5, 6, 7, 7, 7, 8, 9] \]
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Median (Q2): Since there are 20 numbers, the median will be the average of the 10th and 11th values.
- 10th value = 7
- 11th value = 7
- Median (Q2) = (7 + 7) / 2 = 7
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Lower Quartile (Q1): This is the median of the first half of the data (the first 10 numbers).
- The first half is [2, 2, 2, 2, 3, 4, 5, 6, 7, 7].
- The median of this subset is the average of the 5th and 6th values.
- 5th value = 3
- 6th value = 4
- Lower Quartile (Q1) = (3 + 4) / 2 = 3.5
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Upper Quartile (Q3): This is the median of the second half of the data (the last 10 numbers).
- The second half is [7, 7, 8, 9].
- The median of this subset is the average of the 5th and 6th values.
- 5th value = 7
- 6th value = 8
- Upper Quartile (Q3) = (8 + 7) / 2 = 7.5
Thus, we find:
- Lower Quartile (Q1): 3.5
- Median (Q2): 7
- Upper Quartile (Q3): 7.5