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Measures of Variation Practice
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Question
Consider the following dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25. What is the third quartile’s value? Express your answer as a decimal rounded to the nearest tenth.(1 point)

Remaining Attempts : 3
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Answer 1

To find the third quartile (Q3) of the dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25, follow these steps:

1. **Order the Data**: First, we need to sort the dataset in ascending order:
- Ordered dataset: 18, 20, 22, 22, 24, 25, 29, 30, 31

2. **Find the Median**: The median (Q2) divides the dataset into two halves. Since there are 9 data points (an odd number), the median is the middle value:
- Median (Q2) = 24 (the 5th value in the ordered dataset)

3. **Find the Third Quartile (Q3)**: Q3 is the median of the upper half of the data. The upper half consists of the values above the median:
- Upper half: 25, 29, 30, 31

Since there are 4 values, the median of this subset is the average of the 2nd and 3rd values:
- Q3 = (29 + 30) / 2 = 29.5

Therefore, the third quartile’s value is **29.5**.