What is the third quartile, Q3, of the following distribution?
27, 18, 20, 21, 29, 33, 12, 14, 34, 10, 16, 21, 22, 24, 26
A. 24
B. 18
C. 27
D. 4
E. 31
27
Arrange in order of value. 75% of the scores should have a value ≤ that value (Q3).
To find the third quartile, Q3, of a distribution, you first need to arrange the numbers in ascending order:
10, 12, 14, 16, 18, 20, 21, 21, 22, 24, 26, 27, 29, 33, 34
Next, you divide the data set into two halves. Q3 is the median of the upper half. Since there are 15 numbers in the data set, the median of the upper half will be the 8th value.
The 8th value in the data set is 27.
Therefore, the correct answer is C. 27.