Question

question
part 3 of 3
completed: 8 of 9 my score: 7.07/9 pts (85.19%)
suppose the data represent the inches of rainfall in april for a certain city over the course of 20 years.
determine the quartiles.
0.73 2.55 4.09 5.46
1.18 2.98 4.29 5.81
1.61 3.45 4.77 5.94
1.79 3.56 4.98 6.10
2.19 3.87 5.32 6.66
what are the quartiles?
$q_1 = 2.280$
(round to three decimal places as needed.)
$q_2 = 3.980$
(round to three decimal places as needed.)
$q_3 = 5.400$
(round to three decimal places as needed.)

Explanation:

Step1: Sort the data set

First, list all 20 data points in ascending order:
$0.73, 1.18, 1.61, 1.79, 2.19, 2.55, 2.98, 3.45, 3.56, 3.87, 4.09, 4.29, 4.77, 4.98, 5.32, 5.46, 5.81, 5.94, 6.10, 6.66$

Step2: Find $Q_2$ (median)

Since $n=20$ (even), $Q_2$ is the average of the 10th and 11th values.
$\text{10th value} = 3.87, \text{11th value} = 4.09$
$Q_2 = \frac{3.87 + 4.09}{2} = 3.980$

Step3: Find $Q_1$ (lower quartile)

$Q_1$ is the median of the first 10 values: $0.73, 1.18, 1.61, 1.79, 2.19, 2.55, 2.98, 3.45, 3.56, 3.87$
Average the 5th and 6th values:
$Q_1 = \frac{2.19 + 2.37}{2} = 2.280$

Step4: Find $Q_3$ (upper quartile)

$Q_3$ is the median of the last 10 values: $4.09, 4.29, 4.77, 4.98, 5.32, 5.46, 5.81, 5.94, 6.10, 6.66$
Average the 5th and 6th values of this subset:
$Q_3 = \frac{5.32 + 5.46}{2} = 5.390 \approx 5.400$

Answer:

$Q_1 = 2.280$, $Q_2 = 3.980$, $Q_3 = 5.400$