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
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: https://brainly.com/question/24805469
