Question

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Measures of Variation Quick Check
2 of 52 of 5 Items

Question
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
53.3
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Answer 1

To find the third quartile (Q3) in the dataset, you first need to arrange the numbers in ascending order:

1. **Arrange the data**:
- The original dataset is: 53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5
- Sorted in ascending order: 45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3

2. **Find the median (Q2)**:
- Since there are 8 numbers (an even number), the median will be the average of the 4th and 5th numbers.
- 4th number = 47.5, 5th number = 48.1
- Median (Q2) = (47.5 + 48.1) / 2 = 47.8

3. **Find Q3**:
- Q3 is the median of the upper half of the dataset. The upper half is: 48.1, 49.7, 52.1, 53.3
- There are 4 numbers in the upper half, so the median will be the average of the 2nd and 3rd numbers.
- 2nd number = 49.7, 3rd number = 52.1
- Q3 = (49.7 + 52.1) / 2 = 50.9

Therefore, the third quartile (Q3) is **50.9**.