Question

find the first and third quartile for the data shown\
x\
1.2\
3.4\
8.2\
16.8\
19.7\
23.5\
26.9\
27.6\
27.7\
28.6\
\\( q_1 = \\)\
\\( q_3 = \\)

Explanation:

Step1: Confirm sorted data

Data: $1.2, 3.4, 8.2, 16.8, 19.7, 23.5, 26.9, 27.6, 27.7, 28.6$ ($n=10$)

Step2: Calculate $Q_1$ position

$\text{Position of } Q_1 = \frac{n+1}{4} = \frac{10+1}{4} = 2.75$

Step3: Compute $Q_1$ value

$Q_1 = 3.4 + 0.75\times(8.2-3.4) = 8.2$

Step4: Calculate $Q_3$ position

$\text{Position of } Q_3 = \frac{3(n+1)}{4} = \frac{3(10+1)}{4} = 8.25$

Step5: Compute $Q_3$ value

$Q_3 = 27.6 + 0.25\times(27.7-27.6) = 27.6$

Answer:

$Q_1 = 8.2$, $Q_3 = 27.6$