Math / Data & Statistics

QuestionThe prices of the 19 top-rated all-season tires for a specific tire size, are as follows. Answer parts (a) - (c). \begin{tabular}{llllllllll} $\$ 88$ & $\$ 118$ & $\$ 97$ & $\$ 79$ & $\$ 82$ & $\$ 92$ & $\$ 94$ & $\$ 89$ & $\$ 94$ & $\$ 81$ \\ $\$ 109$ & $\$ 115$ & $\$ 103$ & $\$ 95$ & $\$ 85$ & $\$ 92$ & $\$ 75$ & $\$ 99$ & $\$ 91$ & \end{tabular} a) Determine $Q_{2}$ . $\mathrm{Q}_{2}=$ $\square$ b) Determine $Q_{1}$ . $Q_{1}=$ $\square$ c) Determine $Q_{3}$ . $Q_{3}=$ $\square$

Studdy Solution

STEP 1

1. The dataset consists of 19 tire prices.
2. Quartiles divide the dataset into four equal parts.
3. $Q_2$ is the median of the dataset.
4. $Q_1$ is the median of the first half of the dataset.
5. $Q_3$ is the median of the second half of the dataset.

STEP 2

1. Order the data points.
2. Determine $Q_2$ .
3. Determine $Q_1$ .
4. Determine $Q_3$ .

STEP 3

List the tire prices:
$88, 118, 97, 79, 82, 92, 94, 89, 94, 81, 109, 115, 103, 95, 85, 92, 75, 99, 91$

STEP 4

Order the tire prices:
$75, 79, 81, 82, 85, 88, 89, 91, 92, 92, 94, 94, 95, 97, 99, 103, 109, 115, 118$

STEP 5

Determine $Q_2$ , the median of the dataset. Since there are 19 values, the median is the 10th value.
$Q_2 = 92$

STEP 6

Determine $Q_1$ , the median of the first half of the dataset (first 9 values):
$75, 79, 81, 82, 85, 88, 89, 91, 92$
The median is the 5th value.
$Q_1 = 85$

STEP 7

Determine $Q_3$ , the median of the second half of the dataset (last 9 values):
$94, 94, 95, 97, 99, 103, 109, 115, 118$
The median is the 5th value.
$Q_3 = 99$
The quartiles are:
$Q_2 = \boxed{92}$ $Q_1 = \boxed{85}$ $Q_3 = \boxed{99}$

Was this helpful?

Studdy Solution

STEP 1

1. The dataset consists of 19 tire prices.
2. Quartiles divide the dataset into four equal parts.
3. $Q_2$ is the median of the dataset.
4. $Q_1$ is the median of the first half of the dataset.
5. $Q_3$ is the median of the second half of the dataset.

STEP 2

1. Order the data points.
2. Determine $Q_2$ .
3. Determine $Q_1$ .
4. Determine $Q_3$ .

STEP 3

List the tire prices:
$88, 118, 97, 79, 82, 92, 94, 89, 94, 81, 109, 115, 103, 95, 85, 92, 75, 99, 91$

STEP 4

Order the tire prices:
$75, 79, 81, 82, 85, 88, 89, 91, 92, 92, 94, 94, 95, 97, 99, 103, 109, 115, 118$

STEP 5

Determine $Q_2$ , the median of the dataset. Since there are 19 values, the median is the 10th value.
$Q_2 = 92$

STEP 6

Determine $Q_1$ , the median of the first half of the dataset (first 9 values):
$75, 79, 81, 82, 85, 88, 89, 91, 92$
The median is the 5th value.
$Q_1 = 85$

STEP 7

Determine $Q_3$ , the median of the second half of the dataset (last 9 values):
$94, 94, 95, 97, 99, 103, 109, 115, 118$
The median is the 5th value.
$Q_3 = 99$
The quartiles are:
$Q_2 = \boxed{92}$ $Q_1 = \boxed{85}$ $Q_3 = \boxed{99}$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The dataset consists of 19 tire prices.2. Quartiles divide the dataset into four equal parts.3. Q2 Q_2 Q2​ is the median of the dataset.4. Q1 Q_1 Q1​ is the median of the first half of the dataset.5. Q3 Q_3 Q3​ is the median of the second half of the dataset.

STEP 2

1. Order the data points.2. Determine Q2 Q_2 Q2​.3. Determine Q1 Q_1 Q1​.4. Determine Q3 Q_3 Q3​.

STEP 3

List the tire prices:88,118,97,79,82,92,94,89,94,81,109,115,103,95,85,92,75,99,91 88, 118, 97, 79, 82, 92, 94, 89, 94, 81, 109, 115, 103, 95, 85, 92, 75, 99, 91 88,118,97,79,82,92,94,89,94,81,109,115,103,95,85,92,75,99,91

STEP 4

Order the tire prices:75,79,81,82,85,88,89,91,92,92,94,94,95,97,99,103,109,115,118 75, 79, 81, 82, 85, 88, 89, 91, 92, 92, 94, 94, 95, 97, 99, 103, 109, 115, 118 75,79,81,82,85,88,89,91,92,92,94,94,95,97,99,103,109,115,118

STEP 5

Determine Q2 Q_2 Q2​, the median of the dataset. Since there are 19 values, the median is the 10th value.Q2=92 Q_2 = 92 Q2​=92

STEP 6

Determine Q1 Q_1 Q1​, the median of the first half of the dataset (first 9 values):75,79,81,82,85,88,89,91,92 75, 79, 81, 82, 85, 88, 89, 91, 92 75,79,81,82,85,88,89,91,92The median is the 5th value.Q1=85 Q_1 = 85 Q1​=85

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The dataset consists of 19 tire prices.
2. Quartiles divide the dataset into four equal parts.
3. $Q_2$ is the median of the dataset.
4. $Q_1$ is the median of the first half of the dataset.
5. $Q_3$ is the median of the second half of the dataset.

1. Order the data points.
2. Determine $Q_2$ .
3. Determine $Q_1$ .
4. Determine $Q_3$ .

List the tire prices:
$88, 118, 97, 79, 82, 92, 94, 89, 94, 81, 109, 115, 103, 95, 85, 92, 75, 99, 91$

Order the tire prices:
$75, 79, 81, 82, 85, 88, 89, 91, 92, 92, 94, 94, 95, 97, 99, 103, 109, 115, 118$

Determine $Q_2$ , the median of the dataset. Since there are 19 values, the median is the 10th value.
$Q_2 = 92$

Determine $Q_1$ , the median of the first half of the dataset (first 9 values):
$75, 79, 81, 82, 85, 88, 89, 91, 92$
The median is the 5th value.
$Q_1 = 85$