Question

what is the first quartile of this data set? 11,12,15,16,17,19,22,24,29,33,38
a. 19
b. 15
c. 11
d. 29

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 11, 12, 15, 16, 17, 19, 22, 24, 29, 33, 38.

Step2: Calculate position of first - quartile

The formula to find the position of the first - quartile ($Q_1$) for a data set of size $n$ is $i=\frac{1}{4}(n + 1)$. Here, $n = 11$. So, $i=\frac{1}{4}(11 + 1)=\frac{12}{4}=3$.

Step3: Identify first - quartile

Since $i = 3$ is an integer, the first - quartile is the 3rd value in the ordered data set. The 3rd value is 15.

Answer:

B. 15