C. Car Company B is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company A.
To determine consistency, one can calculate the range of each data set. Range is the difference between the highest and lowest values in a data set.
For Car Company A: 36 (highest) - 28 (lowest) = 8
For Car Company B: 40 (highest) - 25 (lowest) = 15
Since Car Company B has a lower range, it means that the highway fuel efficiency of its cars is more consistent compared to Car Company A.
The following data sets represent the highway fuel efficiency in miles per gallon (mpg) of randomly selected cars from two car companies. Which company has cars that are most consistent in highway fuel efficiency?
Car Company A: 35, 28, 35, 30, 31, 36, 35, 30
Car Company B: 29, 33, 40, 27, 34, 34, 34, 25
A. Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B
B. Cars from both companies have equally consistent highway fuel efficiency.
C. Car Company B is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company A.
D. Car Company A is more consistent, because the range of highway fuel efficiency of its cars is higher than that of Car Company B.
5 answers
are u sure
I apologize for the mistake in my previous response. Let me correct it.
To determine consistency, we can also calculate the standard deviation for each data set. The lower the standard deviation, the more consistent the data set is.
For Car Company A:
Mean = (35+28+35+30+31+36+35+30) / 8 = 32.375
Variance = ((35-32.375)^2 + (28-32.375)^2 + (35-32.375)^2 + (30-32.375)^2 + (31-32.375)^2 + (36-32.375)^2 + (35-32.375)^2 + (30-32.375)^2) / 8 = 11.68
Standard Deviation = sqrt(11.68) ≈ 3.42
For Car Company B:
Mean = (29+33+40+27+34+34+34+25) / 8 = 31.75
Variance = ((29-31.75)^2 + (33-31.75)^2 + (40-31.75)^2 + (27-31.75)^2 + (34-31.75)^2 + (34-31.75)^2 + (34-31.75)^2 + (25-31.75)^2) / 8 = 18.60
Standard Deviation = sqrt(18.60) ≈ 4.31
Based on the standard deviation values, Car Company A has a lower standard deviation, indicating that its cars are more consistent in highway fuel efficiency compared to Car Company B. Therefore, the correct answer is:
A. Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.
To determine consistency, we can also calculate the standard deviation for each data set. The lower the standard deviation, the more consistent the data set is.
For Car Company A:
Mean = (35+28+35+30+31+36+35+30) / 8 = 32.375
Variance = ((35-32.375)^2 + (28-32.375)^2 + (35-32.375)^2 + (30-32.375)^2 + (31-32.375)^2 + (36-32.375)^2 + (35-32.375)^2 + (30-32.375)^2) / 8 = 11.68
Standard Deviation = sqrt(11.68) ≈ 3.42
For Car Company B:
Mean = (29+33+40+27+34+34+34+25) / 8 = 31.75
Variance = ((29-31.75)^2 + (33-31.75)^2 + (40-31.75)^2 + (27-31.75)^2 + (34-31.75)^2 + (34-31.75)^2 + (34-31.75)^2 + (25-31.75)^2) / 8 = 18.60
Standard Deviation = sqrt(18.60) ≈ 4.31
Based on the standard deviation values, Car Company A has a lower standard deviation, indicating that its cars are more consistent in highway fuel efficiency compared to Car Company B. Therefore, the correct answer is:
A. Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.
are you correct?
My apologies for the confusion in the previous responses. Let's correctly identify which car company has cars that are most consistent in highway fuel efficiency using the standard deviation calculation.
Car Company A:
- Mean = (35 + 28 + 35 + 30 + 31 + 36 + 35 + 30) / 8 = 32.875
- Variance = [(35 - 32.875)^2 + (28 - 32.875)^2 + (35 - 32.875)^2 + (30 - 32.875)^2 + (31 - 32.875)^2 + (36 - 32.875)^2 + (35 - 32.875)^2 + (30 - 32.875)^2] / 8 ≈ 7.61
- Standard Deviation = sqrt(7.61) ≈ 2.76
Car Company B:
- Mean = (29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.25
- Variance = [(29 - 31.25)^2 + (33 - 31.25)^2 + (40 - 31.25)^2 + (27 - 31.25)^2 + (34 - 31.25)^2 + (34 - 31.25)^2 + (34 - 31.25)^2 + (25 - 31.25)^2] / 8 ≈ 15.89
- Standard Deviation = sqrt(15.89) ≈ 3.99
From the correct calculations, it is evident that Car Company A has cars that are more consistent in highway fuel efficiency, as its standard deviation is lower compared to that of Car Company B. Therefore, the correct answer is:
A. Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.
Car Company A:
- Mean = (35 + 28 + 35 + 30 + 31 + 36 + 35 + 30) / 8 = 32.875
- Variance = [(35 - 32.875)^2 + (28 - 32.875)^2 + (35 - 32.875)^2 + (30 - 32.875)^2 + (31 - 32.875)^2 + (36 - 32.875)^2 + (35 - 32.875)^2 + (30 - 32.875)^2] / 8 ≈ 7.61
- Standard Deviation = sqrt(7.61) ≈ 2.76
Car Company B:
- Mean = (29 + 33 + 40 + 27 + 34 + 34 + 34 + 25) / 8 = 31.25
- Variance = [(29 - 31.25)^2 + (33 - 31.25)^2 + (40 - 31.25)^2 + (27 - 31.25)^2 + (34 - 31.25)^2 + (34 - 31.25)^2 + (34 - 31.25)^2 + (25 - 31.25)^2] / 8 ≈ 15.89
- Standard Deviation = sqrt(15.89) ≈ 3.99
From the correct calculations, it is evident that Car Company A has cars that are more consistent in highway fuel efficiency, as its standard deviation is lower compared to that of Car Company B. Therefore, the correct answer is:
A. Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.