The following data set represents the highway fuel efficiency in miles per gallon (mpg) of randomly selected cars from two car companies.

Question

Car Company A: 35, 28, 35, 30, 31, 38, 35, 30
Car Company B: 29, 33, 36, 27, 34, 34, 34, 25

Which of the following statements is true?

(1 point)
Responses

The cars from both companies have the same mean, median, and modal highway fuel efficiency.
The cars from both companies have the same mean, median, and modal highway fuel efficiency.

The cars from Company B have higher modal highway fuel efficiency than Company A.
The cars from Company B have higher modal highway fuel efficiency than Company A.

The cars from Company A have a higher mean highway fuel efficiency that Company B.
The cars from Company A have a higher mean highway fuel efficiency that Company B.

The cars from Company A have higher median highway

Answer 1

To evaluate the statements about the highway fuel efficiency of the cars from Company A and Company B, we will first calculate the mean, median, and mode for each company.

Car Company A:

• Data: 35, 28, 35, 30, 31, 38, 35, 30
• Mean = (35 + 28 + 35 + 30 + 31 + 38 + 35 + 30) / 8 = 32.875
• Median: Order the data: 28, 30, 30, 31, 35, 35, 35, 38. The median is the average of the two middle numbers (31 and 35), which is (31 + 35) / 2 = 33.
• Mode: The mode is 35 (it appears most frequently).

Car Company B:

• Data: 29, 33, 36, 27, 34, 34, 34, 25
• Mean = (29 + 33 + 36 + 27 + 34 + 34 + 34 + 25) / 8 = 30.5
• Median: Order the data: 25, 27, 29, 33, 34, 34, 34, 36. The median is the average of the two middle numbers (29 and 33), which is (29 + 33) / 2 = 31.
• Mode: The mode is 34 (it appears most frequently).

Summary of Findings

• Company A:

  • Mean: 32.875
  • Median: 33
  • Mode: 35

• Company B:

  • Mean: 30.5
  • Median: 31
  • Mode: 34

Evaluating the Statements

1. "The cars from both companies have the same mean, median, and modal highway fuel efficiency."

   • False (the means, medians, and modes are different).

2. "The cars from Company B have higher modal highway fuel efficiency than Company A."

   • False (Company A's mode is 35, which is higher than Company B's mode of 34).

3. "The cars from Company A have a higher mean highway fuel efficiency than Company B."

   • True (Company A's mean is 32.875, which is higher than Company B's mean of 30.5).

4. "The cars from Company A have higher median highway fuel efficiency."

   • True (Company A's median is 33, while Company B's median is 31).

Conclusion

The true statements are:

• "The cars from Company A have a higher mean highway fuel efficiency than Company B."
• "The cars from Company A have higher median highway fuel efficiency."

If you need to select only one option, the most definitive and clear statement that represents the data well is the statement about the mean.

Answer 2

What

Answer 3

I apologize for the confusion. Let's clarify the correct analysis based on the calculations of the means, medians, and modes for both companies. Here’s a concise recap:

Car Company A:

• Data: 35, 28, 35, 30, 31, 38, 35, 30
  • Mean: \( \frac{35 + 28 + 35 + 30 + 31 + 38 + 35 + 30}{8} = 32.875 \)
  • Median: The sorted data is 28, 30, 30, 31, 35, 35, 35, 38. The median (average of the 4th and 5th values) is \( \frac{31 + 35}{2} = 33 \).
  • Mode: 35 (it appears most frequently).

Car Company B:

• Data: 29, 33, 36, 27, 34, 34, 34, 25
  • Mean: \( \frac{29 + 33 + 36 + 27 + 34 + 34 + 34 + 25}{8} = 30.5 \)
  • Median: The sorted data is 25, 27, 29, 33, 34, 34, 34, 36. The median (average of the 4th and 5th values) is \( \frac{29 + 33}{2} = 31 \).
  • Mode: 34 (it appears most frequently).

Summary

• Company A:

  • Mean: 32.875
  • Median: 33
  • Mode: 35

• Company B:

  • Mean: 30.5
  • Median: 31
  • Mode: 34

Evaluation of the Statements:

1. False - The cars from both companies do not have the same mean, median, and mode.
2. False - The modal highway fuel efficiency of Company B (34) is not higher than that of Company A (35).
3. True - The cars from Company A have a higher mean highway fuel efficiency (32.875) than those from Company B (30.5).
4. True - The cars from Company A have a higher median highway fuel efficiency (33) than Company B (31).

Conclusion

Based on the calculations, the correct statement is:

• "The cars from Company A have a higher mean highway fuel efficiency than Company B."

If you're looking for singular confirmation, please let me know!

Answer 4

The randomly selected delivery times (in minutes) of two fast food restaurants are as follows. 

Fast Food 1 Fast Food 2
42 40
38 37
37 40
39 41
38 38
40 46
45 41
41 37
40 40
Which of the following statements is false?

(1 point)
Responses

Both fast food restaurants have exactly one modal delivery time of 40 minutes.
Both fast food restaurants have exactly one modal delivery time of 40 minutes.

Neither data set contains an outlier.
Neither data set contains an outlier.

Both fast food restaurants have the same mean delivery time of 40 minutes. 
Both fast food restaurants have the same mean delivery time of 40 minutes. 

Both fast food restaurants have the same median delivery t

Answer 5

To determine which statement is false regarding the delivery times for the two fast food restaurants, we need to calculate the mean, median, and mode of the data sets provided.

Fast Food 1 Data:

• Times: 42, 38, 37, 39, 38, 40, 45, 41, 40

• Mean: \[ \text{Mean} = \frac{42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40}{9} = \frac{ 42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40}{9} = \frac{ 358}{9} \approx 39.78 \]

• Median: Order the data: 37, 38, 38, 39, 40, 40, 41, 42, 45.
  The median (the 5th value in the ordered list) is 40.

• Mode: The mode is 38 (it appears most frequently, twice).

Fast Food 2 Data:

• Times: 40, 37, 40, 41, 38, 46, 41, 37, 40

• Mean: \[ \text{Mean} = \frac{40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40}{9} = \frac{ 40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40}{9} = \frac{ 360}{9} = 40 \]

• Median: Order the data: 37, 37, 38, 40, 40, 40, 41, 41, 46. The median (the 5th value in the ordered list) is 40.

• Mode: The mode is 40 (it appears most frequently, three times).

Summary of Results:

• Fast Food 1:

  • Mean: ~39.78
  • Median: 40
  • Mode: 38

• Fast Food 2:

  • Mean: 40
  • Median: 40
  • Mode: 40

Evaluating the Statements:

1. "Both fast food restaurants have exactly one modal delivery time of 40 minutes."

   • False for Fast Food 1 (its mode is 38, not 40).

2. "Neither data set contains an outlier."

   • This is True as there are no values significantly different from the rest of the data in both sets.

3. "Both fast food restaurants have the same mean delivery time of 40 minutes."

   • False; Fast Food 1 mean is ~39.78, while Fast Food 2 mean is 40.

4. "Both fast food restaurants have the same median delivery time."

   • True; both medians are 40.

Conclusion:

The false statement(s) are:

1. "Both fast food restaurants have exactly one modal delivery time of 40 minutes."
2. "Both fast food restaurants have the same mean delivery time of 40 minutes."

If you need to identify only one statement as clearly wrong, the most straightforward falsehood is the claim about having the same modal delivery time since Fast Food 1's mode is not 40.