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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.(1
To find the third quartile value, first arrange the dataset in ascending order:
18, 20, 22, 22, 24, 25, 29, 30, 31
There are 9 data points in the dataset, so the third quartile can be calculated as follows:
Q3 = (n+1)/4
Q3 = (9+1)/4
Q3 = 10/4
Q3 = 2.5
Since 2.5 falls between the 2nd and 3rd data points, we can find the third quartile by taking the average of those two data points:
(Q3 = (24 + 25) / 2
Q3 = 49 / 2
Q3 = 24.5
Therefore, the third quartile value in the dataset is 24.5.