To find the third quartile (Q3) of the given data set, we need to first arrange the data in ascending order, which it already is:
14, 18, 20, 21, 25, 32, 38, 42, 48
Next, we'll determine the position of the third quartile. The third quartile is the median of the upper half of the data.
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Finding the median position:
- The median (Q2) divides the data into two halves. Since there are 9 data points (an odd number), the median position is at \( (N + 1) / 2 \) where \( N \) is the total number of data points.
- \( (9 + 1) / 2 = 5 \)
- The median (Q2) is the 5th value in the ordered list, which is 25.
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Splitting the data:
- The lower half of the data (below the median) is: 14, 18, 20, 21 (4 values).
- The upper half of the data (above the median) is: 32, 38, 42, 48 (4 values).
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Finding the third quartile (Q3):
- To find Q3, we need the median of the upper half: 32, 38, 42, 48.
- Since there are 4 values (an even number), the median is the average of the two middle values.
- The two middle values in the upper half are 38 and 42.
- \( Q3 = (38 + 42) / 2 = 80 / 2 = 40 \).
Thus, the third quartile (Q3) of the data set is \( \boxed{40} \).