Question

suppose the data represent the inches of rainfall in april for a certain city over the course of 20 years.
determine the quartiles.
0.58 2.36 3.97 5.56
0.98 2.56 4.18 5.81
1.14 2.67 4.57 6.11
1.53 3.15 4.97 6.54
1.95 3.63 5.21 6.69
what are the quartiles?
$q_1 = 2.155$
(round to three decimal places as needed.)
$q_2 = \square$
(round to three decimal places as needed.)

Explanation:

Step1: Sort the data set

First, arrange all 20 data points in ascending order:
$0.58, 0.98, 1.14, 1.53, 1.95, 2.36, 2.56, 2.67, 3.15, 3.63, 3.97, 4.18, 4.57, 4.97, 5.21, 5.56, 5.81, 6.11, 6.54, 6.69$

Step2: Find position of $Q_2$

$Q_2$ (the median) is the average of the values at positions $\frac{n}{2}$ and $\frac{n}{2}+1$ for even $n=20$.
Positions: $\frac{20}{2}=10$ and $10+1=11$

Step3: Calculate $Q_2$

Take the average of the 10th and 11th values:
$$Q_2 = \frac{3.63 + 3.97}{2}$$
$$Q_2 = \frac{7.6}{2} = 3.8$$

Answer:

$Q_2 = 3.800$