Question

the prices of the 19 top-rated all-season tires for a specific tire size, are as follows. answer parts (a) - (c).

$88 $117 $98 $78 $82 $90 $91 $89 $91 $81
$109 $112 $101 $96 $85 $90 $75 $99 $90

a) determine \\(q_2\\).
\\(q_2 = 90\\)

b) determine \\(q_1\\).
\\(q_1 = \\)

Explanation:

Sort the dataset in ascending order

Using the Quartiles knowledge point
The given dataset of \(19\) tire prices is:
\(88, 117, 98, 78, 82, 90, 91, 89, 91, 81, 109, 112, 101, 96, 85, 90, 75, 99, 90\)

Sorting these \(19\) values from smallest to largest:
\(75, 78, 81, 82, 85, 88, 89, 90, 90, 90, 91, 91, 96, 98, 99, 101, 109, 112, 117\)

Find the median (Q2)

Using the Second Quartile knowledge point

$$
LATEXBLOCK0
$$

Identify the lower half of the dataset

To find \(Q_1\), we look at the values strictly below the median position (the first \(9\) values):
\(75, 78, 81, 82, 85, 88, 89, 90, 90\)

Calculate the first quartile (Q1)

The first quartile \(Q_1\) is the median of this lower half of \(9\) values:

$$
LATEXBLOCK1
$$

Answer:

b) Determine \(Q_1\).

\(Q_1 =\) <blank>85</blank>