Consider the following dataset: 22. 29. 31. 30, 22, 24, 18, 20, 25. What is the third quartile's value? Round to the nearest tenth if necessary.
To find the third quartile (Q3), we first need to arrange the data in ascending order:
18, 20, 22, 22, 24, 25, 29, 30, 31
Since there are 9 data points, the position of Q3 is given by (3/4)(n+1) = (3/4)(9+1) = (3/4)(10) = 7.5.
This means that the third quartile falls between the 7th and 8th values in the ordered dataset. To find the exact value, we take the average of these two values:
Q3 = (25 + 29) / 2 = 27
Therefore, the third quartile's value is 27.