Question

find the quartiles for the following set of data.
data 3 5 7 9 11 12 14 15 17
q1=
q2=
q3=

Explanation:

Step1: Calculate the position of Q2 (median)

The data set has $n = 9$ values. The position of the median $Q_2$ is $\frac{n + 1}{2}=\frac{9+1}{2}=5$. So $Q_2$ is the 5 - th value in the ordered data set.

Step2: Determine Q2

$Q_2=11$

Step3: Split data for Q1

The lower - half of the data set (excluding $Q_2$) is $3,5,7,9$. The number of values in the lower - half $n_1=4$. The position of $Q_1$ is $\frac{n_1 + 1}{2}=\frac{4+1}{2}=2.5$. So $Q_1=\frac{5 + 7}{2}=6$.

Step4: Split data for Q3

The upper - half of the data set (excluding $Q_2$) is $12,14,15,17$. The number of values in the upper - half $n_2 = 4$. The position of $Q_3$ is $\frac{n_2+1}{2}=\frac{4 + 1}{2}=2.5$. So $Q_3=\frac{14+15}{2}=14.5$.

Answer:

$Q_1 = 6$
$Q_2 = 11$
$Q_3 = 14.5$