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 = 85\\)

c) determine \\(q_3\\).
\\(q_3 = \\)

Explanation:

Sort the dataset in ascending order

Using the Quartiles knowledge point

$$ \text{Sorted data: } 75, 78, 81, 82, 85, 88, 89, 90, 90, 90, 91, 91, 96, 98, 99, 101, 109, 112, 117 $$

Identify the median (Q2)

Using the Second Quartile knowledge point

$$
LATEXBLOCK0
$$

Identify the first quartile (Q1)

Using the First Quartile Calculation knowledge point

$$
LATEXBLOCK1
$$

Calculate the third quartile (Q3)

To find the third quartile \(Q_3\), we locate the median of the upper half of the dataset. The upper half consists of the 9 values strictly above the median position:

$$ 91, 91, 96, 98, 99, 101, 109, 112, 117 $$

The median of these 9 values is the 5th value in this upper subset:

$$ \text{Position of } Q_3 = 10 + 5 = 15\text{ in the sorted list} $$

$$ Q_3 = 99 $$

Answer:

c) Determine \(Q_3\).

\(Q_3 =\) <blank>99</blank>