To find the third quartile (Q3) of the dataset, we first need to arrange the numbers in ascending order:
18, 20, 22, 22, 24, 25, 30, 31, 29
Correctly ordered, the dataset is: 18, 20, 22, 22, 24, 25, 29, 30, 31
Next, we find the quartiles. The first step is to determine the median (Q2) since the quartiles are based around the median.
The median is the middle value of the dataset. Since there are 9 values (an odd number), the median is the value at position (9 + 1)/2 = 5:
Median (Q2) = 24
Now, we find Q1 (the first quartile) and Q3 (the third quartile).
To find Q1, we look at the lower half of the dataset (the first four values): 18, 20, 22, 22
Since there are 4 numbers (an even number), Q1 will be the average of the 2nd and 3rd values: Q1 = (20 + 22) / 2 = 21
Now, we find Q3. We look at the upper half of the dataset (the last four values): 25, 29, 30, 31
Again, since there are 4 numbers, Q3 will be the average of the 2nd and 3rd values: Q3 = (29 + 30) / 2 = 29.5
Therefore, the third quartile's value is 29.5.