Identify the third quartile in the following dataset:
53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5(1 point)
Responses
50.9
50.9
47.05
47.05
47.8
47.8
53.3
50.9
To identify the third quartile in the given dataset, we need to arrange the numbers in ascending order:
45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3
The third quartile is the median of the upper half of the data. Since we have 8 numbers, the upper half consists of the last 4 numbers:
48.1, 49.7, 52.1, 53.3
To find the median of these numbers, we take the average of the middle two values:
(49.7 + 52.1)/2 = 101.8/2 = 50.9
Therefore, the third quartile in the given dataset is 50.9.
To identify the third quartile in a dataset, you need to arrange the data in ascending order. Once the data is sorted, you can determine the position of the third quartile. The third quartile marks the boundary below which 75% of the data falls.
Let's rearrange the dataset in ascending order:
45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3
With this sorted dataset, we can find the position of the third quartile. Since there are 8 data points, the position of the third quartile is given by:
Position = (3/4) * (n + 1)
= (3/4) * (8 + 1)
= (3/4) * 9
= 6.75
Since the position is not a whole number, we need to take the average of the data at positions 6 and 7:
Third quartile = (data at position 6 + data at position 7) / 2
= (52.1 + 53.3) / 2
= 105.4 / 2
= 52.7
Therefore, the third quartile in the given dataset is approximately 52.7.