To find the third quartile (Q3) in the dataset, we first need to sort the data in ascending order:
Here is the sorted dataset:
45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3
Next, we need to determine the position of Q3, which is the median of the upper half of the data. Since there are 8 numbers in the dataset, the upper half consists of the last four numbers:
Upper half: 48.1, 49.7, 52.1, 53.3
To find Q3, we calculate the median of the upper half. Since there are 4 numbers:
The two middle numbers are 49.7 and 52.1.
Now, we calculate the median of these two numbers:
Q3 = (49.7 + 52.1) / 2 = 101.8 / 2 = 50.9
So the third quartile (Q3) is 50.9.
Thus, the correct response is:
50.9