Question

1. Find the quartiles for the tire pressures of car tires at an auto clinic. Tire pressure is measured in psi

Answer 1

The quartiles and outliers for the data provided are as follows:

1. Quartiles for the tire pressures of car tires at an auto clinic:

• Q2 = 28 psi
• Q4 = 36 psi
• Q1 = 21.5 psi
• Q3 = 34 psi

2. The outlier(s) for the tires prices is $450

3. The outlier(s) for the tires prices is $650

4. The outlier(s) for the tires prices is $540

5. Quartiles for the tire pressures of car tires at an auto clinic are:

• Q2 = 27 psi
• Q4 = 35 psi
• Q1 = 23.5 psi
• Q3 = 33 psi

Quartiles

• Quartiles are the values that divide a list of numbers into four parts or quarters after the numbers are arranged in ascending order.

They describe the dispersionof a set of data values.

• Q1 is the first quartile or lower quartile. 25% of the numbers in the data set are at or below Q1.
• Q2 is the second quartile. 50% of the numbers are below Q2, and
• Q3 is the third quartile, or upper quartile. 75% of the numbers are at or below Q3.
• Q4 is the maximum value in the data set. 100% of the numbers are at or below Q4.

Outliers

Outliers are data points that differs significantly from other observations.

There are two outliers: lower boundary outliers and upper boundary outliers.

• Formula for lower boundary outliers is:

Q1 − 1.5(IQR)

• Formula for upper boundary outliers is:

Q3 + 1.5(IQR)

where IQR is interquartile range

• IQR = Q3 - Q1

1. Quartiles for the tire pressures of car tires at an auto clinic: (20, 27,19, 23, 29, 28, 34, 34, 36)

Arranging in increasing order:

19, 20, 23, 27, 28, 29, 34, 34, 36.

Q2 = 28

Q4 = 36

Q1 = (20 + 23) / 2

Q1 = 21.5

Q3 = (34 + 34) /2

Q3 = 34

2. Outlier(s) for these tires prices: $58, $95, $78, $125, $87, $158, $152, $182, $195, $450

Arranging in increasing order:

58, 78, 87, 95, 125, 152, 158, 182, 195, 450

Q1 = (87 + 78)/2

Q1 = 62.5

Q3 = 182 + 195/2

Q3 = 188.5

IQR = 188.5 - 62.5

IQR = 126

Lower boundary outlier(s) = 62.5 - 1.5(126)

Lower boundary outliers = -126.5

Thus there are no lower outliers.

Upper boundary outliers = 188.5 + 1.5(126)

Upper boundary outliers = 377.5

Therefore, 450 is an outlier.

3. The outlier(s) for these tires prices: $78, $195, $98, $145, $87, $138, $159, $172, $155, $210, $240, $650

Arranging in increasing order:

78, 87, 98, 138, 145, 155, 159, 172, 195, 210, 240, 650

Q1 = 98

Q3 = 210

IQR = 210 - 98

IQR = 112

Lower boundary outlier(s) = 98 - 1.5(168)

Lower boundary outliers = -70

Thus there are no lower outliers.

Upper boundary outliers = 210 + 1.5(112)

Upper boundary outliers = 378

Therefore, 650 is an outlier.

4. The outlier(s) for these tires prices: $88, $135, $75, $135, $85, $168, $156, $192, $195, $210, $230, $245, $540

Arranging in increasing order:

75, 85, 88, 135, 135, 156, 168, 192, 195, 210, 230, 245, 540

Q1 = (88 + 135)/2

Q1 = 111.5

Q3 = (210 + 230)/2

Q3 = 220

IQR = 220 - 111.5

IQR = 108.5

Lower boundary outlier(s) = 111.5 - 1.5(108.5)

Lower boundary outliers = - 51.25

Thus, there are no lower outliers.

Upper boundary outliers = 220 + 1.5(111.5)

Upper boundary outliers = 387.25

Therefore, 540 is an outlier.

5. Quartiles for the tire pressures of car tires at an auto clinic: 23, 29,18, 24, 27, 24, 35, 32, 34

Arranging in increasing order:

18, 23, 24, 24, 27, 29, 32, 34, 35.

Q2 = 27

Q4 = 35

Q1 = (23 + 24) / 2

Q1 = 23.5

Q3 = (32 + 34) /2

Q3 = 33

Learn more about quartiles and outliers at: brainly.com/question/24805469