Question

what is the third quartile of this data set? 20,21,24,25,28,29,35,37,42,43,44
a. 44
b. 24
c. 42
d. 29

Explanation:

Step1: Arrange data in order

The data is already in ascending order: 20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44.

Step2: Calculate position of third - quartile

The formula to find the position of the third - quartile ($Q_3$) for a data set of size $n$ is $i=\frac{3(n + 1)}{4}$. Here, $n = 11$. So, $i=\frac{3\times(11 + 1)}{4}=\frac{3\times12}{4}=9$.

Step3: Find the third - quartile

Since $i = 9$ is an integer, the third - quartile is the 9th value in the ordered data set. The 9th value is 42.

Answer:

C. 42