The ages, in years, of randomly selected employees are 34, 41, 28, 35, 27, 44, 48, 29, 33, and 39. Determine the mean age.(1 point)
The mean age is:
$$\frac{34 + 41 + 28 + 35 + 27 + 44 + 48 + 29 + 33 + 39}{10} = \frac{348}{10} = \boxed{34.8}$$
For 10 consecutive days, Anthony recorded the daily high temperatures in Dayton and Laredo. The table shows the data.
Daily High Temperatures (in °F)
Dayton 77 82 85 87 90 85 79 86 91 88
Laredo 81 79 80 86 88 92 82 88 84 87
Which city has a higher median daily high temperature? How much higher is this city’s median than the other city’s median daily high temperature?
(1 point)
To find the median, we need to put the temperatures in order first:
Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
For Dayton, the median is the middle number. Since we have 10 temperatures, the middle is between the 5th and 6th numbers, which are both 85. So the median for Dayton is 85.
For Laredo, the median is also the middle number. Again, we have 10 temperatures, so the middle is between the 5th and 6th numbers, which are 84 and 86. So the median for Laredo is 85.
Both cities have the same median daily high temperature of 85 degrees Fahrenheit.
The following data set represents the highway fuel efficiency in miles per gallon (mpg) of randomly selected cars from two car companies.
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?
A. The cars from Company B have higher modal highway fuel efficiency than Company A.
B. The cars from Company A have higher median highway fuel efficiency than Company B.
C. The cars from both companies have the same mean, median, and modal highway fuel efficiency.
D. The cars from Company A have a higher mean highway fuel efficiency that Company B.
(1 point)
A. The cars from Company B have higher modal highway fuel efficiency than Company A.
The mode is the most frequently occurring value in the data set. For Company A, the mode is 35 since it appears three times. For Company B, the mode is 34 since it appears three times, which is higher than the mode of Company A.
B. The cars from Company A have higher median highway fuel efficiency than Company B.
To find the median, we need to put the data in order:
Company A: 28, 30, 30, 31, 35, 35, 35, 38
Company B: 25, 27, 29, 33, 34, 34, 34, 36
For Company A, the median is the middle value, which is 33. For Company B, the median is also 33. Therefore, neither company has a higher median highway fuel efficiency than the other.
C. The cars from both companies have the same mean, median, and modal highway fuel efficiency.
This statement is incorrect because we have already found that the modal highway fuel efficiency for each company is different.
D. The cars from Company A have a higher mean highway fuel efficiency than Company B.
To find the mean, we add up all the values and divide by the number of values:
Company A: (35 + 28 + 35 + 30 + 31 + 38 + 35 + 30) / 8 = 32.125
Company B: (29 + 33 + 36 + 27 + 34 + 34 + 34 + 25) / 8 = 31.5
Therefore, Company A has a higher mean highway fuel efficiency than Company B.
So statement D is true.
For 10 consecutive days, Anthony recorded the daily high temperatures in Dayton and Laredo. The table shows the data.
Daily High Temperatures (in °F)
Dayton 77 82 85 87 90 85 79 86 91 88
Laredo 81 79 80 86 88 92 82 88 84 87
Which city has a higher median daily high temperature? How much higher is this city’s median than the other city’s median daily high temperature?
A. Laredo has a higher median daily high temperature than Dayton by 0.5°F.
B. Laredo has a higher median daily high temperature than Dayton by 1°F.
C. Dayton has a higher median daily high temperature than Laredo by 0.3°F.
D. Dayton has a higher median daily high temperature than Laredo by 0.5°F.
(1 point)
The median for Dayton is 85, and the median for Laredo is also 85. Therefore, neither city has a higher median daily high temperature than the other.
So the answer is none of the above.
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?
A. Both fast food restaurants have exactly one modal delivery time of 40 minutes.
B. Both fast food restaurants have the same mean delivery time of 40 minutes.
C. Both fast food restaurants have the same median delivery time of 40 minutes.
D. Neither data set contains an outlier.
(1 point)
A. Both fast food restaurants have exactly one modal delivery time of 40 minutes.
This statement is false. Fast Food 1 has two modes of 38 and 40, and Fast Food 2 has two modes of 37 and 40.
B. Both fast food restaurants have the same mean delivery time of 40 minutes.
To calculate the mean, we add up all the delivery times and divide by the sample size:
Fast Food 1: (42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40) / 9 = 39.22 minutes
Fast Food 2: (40 + 37 + 40 + 41 + 38 + 46 + 41 + 37 + 40) / 9 = 39.22 minutes
Therefore, both fast food restaurants have the same mean delivery time of approximately 39.22 minutes. This statement is true.
C. Both fast food restaurants have the same median delivery time of 40 minutes.
For Fast Food 1, the median is 39, and for Fast Food 2, the median is 40. Therefore, both fast food restaurants do not have the same median delivery time. This statement is false.
D. Neither data set contains an outlier.
We can check for outliers by using the interquartile range (IQR).
For Fast Food 1:
- The lower quartile (Q1) is 38.
- The upper quartile (Q3) is 42.
- The IQR is Q3 - Q1 = 4.
- The lower outlier threshold is Q1 - 1.5(IQR) = 32.
- The upper outlier threshold is Q3 + 1.5(IQR) = 48.
All of the delivery times for Fast Food 1 are within the outlier thresholds, so there are no outliers.
For Fast Food 2:
- The lower quartile (Q1) is 38.
- The upper quartile (Q3) is 41.5.
- The IQR is Q3 - Q1 = 3.5.
- The lower outlier threshold is Q1 - 1.5(IQR) = 32.25.
- The upper outlier threshold is Q3 + 1.5(IQR) = 47.25.
All of the delivery times for Fast Food 2 are within the outlier thresholds, so there are no outliers.
Therefore, neither data set contains an outlier. This statement is true.
So the false statement is A.
To find the mean age, you need to calculate the average of all the ages.
Here's how you can do it:
1. Add up all the ages: 34 + 41 + 28 + 35 + 27 + 44 + 48 + 29 + 33 + 39 = 358.
2. Count the number of ages given, which is 10.
3. Divide the sum of ages (358) by the number of ages (10): 358 ÷ 10 = 35.8.
Therefore, the mean age of the randomly selected employees is 35.8 years.