To find the third quartile (Q3) of the dataset, we first need to arrange the data in ascending order. The dataset is:
53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5
Arranging it in ascending order gives us:
45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3
Next, to find the third quartile, we determine Q3, which is the value that cuts off the highest 25% of the data.
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The median (Q2) for this dataset, which has 8 values, is the average of the 4th and 5th values:
\[ Q2 = \frac{47.5 + 48.1}{2} = \frac{95.6}{2} = 47.8 \]
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Now, we find Q3 by looking at the upper half of the dataset (values above the median):
The upper half consists of: 48.1, 49.7, 52.1, 53.3
Q3 is the median of this upper half: \[ Q3 = \frac{49.7 + 52.1}{2} = \frac{101.8}{2} = 50.9 \]
Thus, the third quartile (Q3) of the dataset is 50.9.
So the correct answer is:
50.9