To find the third quartile (Q3) of the dataset, we must first arrange the data in ascending order (which is already done in this case):
14, 18, 20, 21, 25, 32, 42, 46, 48
Next, we need to find the median (Q2) of the dataset to identify the position for Q3. For a dataset of 9 values, the median is the value in the 5th position:
- Median (Q2) = 25
The third quartile (Q3) is the median of the upper half of the dataset. The upper half consists of the numbers above the median:
32, 42, 46, 48
Now we find the median of this upper half:
- The upper half has 4 numbers, so the median (Q3) is the average of the 2nd and 3rd values:
- Q3 = (42 + 46) / 2 = 88 / 2 = 44
Therefore, the third quartile (Q3) is 44.
So, the correct answer is: 44