To find the third quartile (Q3) of the dataset, we first need to sort the data in ascending order and then determine the value that separates the highest 25% of the data.
Given dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25
First, let's sort the dataset: 18, 20, 22, 22, 24, 25, 29, 30, 31
Now, the sorted dataset has 9 values. The third quartile (Q3) is the value at the 75th percentile position. To find the position, we can use the formula:
\[ Q_k = \frac{k(n+1)}{4} \]
where \( k \) is the quartile number (for Q3, \( k = 3 \)), and \( n \) is the number of observations (in this case, \( n = 9 \)).
Calculating the position: \[ Q_3 = \frac{3(9+1)}{4} = \frac{30}{4} = 7.5 \]
Since this is a non-integer, we take the average of the values at the 7th and 8th positions in the sorted list.
- 7th value: 29
- 8th value: 30
Now we calculate the average: \[ Q3 = \frac{29 + 30}{2} = \frac{59}{2} = 29.5 \]
Therefore, the value of the third quartile (Q3) is 29.5.