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?
$q_1=\square$
(round to three decimal places as needed.)

Explanation:

Step1: Sort the data set

First, arrange all 20 data points in ascending order:
$0.58, 0.98, 1.14, 1.53, 1.95, 2.36, 2.56, 2.67, 3.15, 3.63, 3.97, 4.18, 4.57, 4.97, 5.21, 5.58, 5.81, 6.11, 6.54, 6.69$

Step2: Find median (Q2) to split data

The median is the average of the 10th and 11th values:
$\text{Q2} = \frac{3.63 + 3.97}{2} = 3.8$
This splits the data into a lower half (first 10 values) and upper half (last 10 values).

Step3: Calculate Q1 from lower half

Q1 is the median of the lower half (first 10 values: $0.58, 0.98, 1.14, 1.53, 1.95, 2.36, 2.56, 2.67, 3.15, 3.63$). Average the 5th and 6th values:
$\text{Q1} = \frac{1.95 + 2.36}{2} = 2.155$

Answer:

$\text{Q}_1 = 2.155$