To find the mean number of hours students spent on math homework, we need to calculate the total number of hours spent by all students and then divide it by the total number of students.
Total hours = (1*8) + (2*6) + (3*4) + (4*2) + (5*1) = 8 + 12 + 12 + 8 + 5 = 45 hours
Total number of students = 8 + 6 + 4 + 2 + 1 = 21 students
Mean number of hours spent = Total hours / Total number of students
Mean number of hours spent = 45 hours / 21 students = 2.14 hours
Therefore, the mean number of hours students spent on math homework is 2.14 hours.
So the correct answer is
2.14 hours.
Use the image to answer the question.
A bar graph shows the number of hours spent on math homework versus the number of students. The horizontal axis shows the time in hours ranging from 1 to 5 in increments of 1. The vertical axis shows the number of students ranging from 0 to 10 in increments of 1. The data with time in hours, followed by the number of students is as follows: 1 to 8, 2 to 6, 3 to 4, 4 to 2, and 5 to 1.
The graph shows the number of hours randomly selected students spent on math homework. What is the mean number of hours students spent on math homework?
(1 point)
Responses
9 hours
9 hours
1.4 hours
1.4 hours
1 hour
1 hour
2.14 hours
2.14 hours
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5 answers
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)
Responses
Laredo has a higher median daily high temperature than Dayton by 1°F.
Laredo has a higher median daily high temperature than Dayton by 1 degree F.
Laredo has a higher median daily high temperature than Dayton by 0.5°F.
Laredo has a higher median daily high temperature than Dayton by 0.5 degree F.
Dayton has a higher median daily high temperature than Laredo by 0.3°F.
Dayton has a higher median daily high temperature than Laredo by 0.3 degree F.
Dayton has a higher median daily high temperature than Laredo by 0.5°F.
Dayton has a higher median daily high temperature than Laredo by 0.5 degree F.
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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)
Responses
Laredo has a higher median daily high temperature than Dayton by 1°F.
Laredo has a higher median daily high temperature than Dayton by 1 degree F.
Laredo has a higher median daily high temperature than Dayton by 0.5°F.
Laredo has a higher median daily high temperature than Dayton by 0.5 degree F.
Dayton has a higher median daily high temperature than Laredo by 0.3°F.
Dayton has a higher median daily high temperature than Laredo by 0.3 degree F.
Dayton has a higher median daily high temperature than Laredo by 0.5°F.
Dayton has a higher median daily high temperature than Laredo by 0.5 degree F.
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To find the median daily high temperature for each city, we first need to arrange the temperatures in ascending order:
For Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
For Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
Now we find the median temperature for each city. Since each city has 10 temperatures, the median will be the average of the middle two temperatures.
For Dayton, the median is the average of the 5th and 6th temperatures:
Median for Dayton = (85 + 86) / 2 = 85.5°F
For Laredo, the median is the average of the 5th and 6th temperatures:
Median for Laredo = (84 + 86) / 2 = 85°F
Therefore, Laredo has a higher median daily high temperature than Dayton by 0.5°F.
So the correct answer is:
Laredo has a higher median daily high temperature than Dayton by 0.5°F.
For Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
For Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
Now we find the median temperature for each city. Since each city has 10 temperatures, the median will be the average of the middle two temperatures.
For Dayton, the median is the average of the 5th and 6th temperatures:
Median for Dayton = (85 + 86) / 2 = 85.5°F
For Laredo, the median is the average of the 5th and 6th temperatures:
Median for Laredo = (84 + 86) / 2 = 85°F
Therefore, Laredo has a higher median daily high temperature than Dayton by 0.5°F.
So the correct answer is:
Laredo has a higher median daily high temperature than Dayton by 0.5°F.
Measures of Center Quick Check
4 of 54 of 5 Items
Question
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?
(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 A have higher median highway fuel efficiency than Company B.
The cars from Company A have higher median highway fuel efficiency than Company B.
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 B have higher modal highway fuel efficiency than Company A.
The cars from Company B have higher modal highway fuel efficiency than Company A.
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4 of 54 of 5 Items
Question
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?
(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 A have higher median highway fuel efficiency than Company B.
The cars from Company A have higher median highway fuel efficiency than Company B.
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 B have higher modal highway fuel efficiency than Company A.
The cars from Company B have higher modal highway fuel efficiency than Company A.
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To determine which statement is true, we need to calculate the mean, median, and mode for each set of data.
For Car Company A:
Mean fuel efficiency = (35 + 28 + 35 + 30 + 31 + 38 + 35 + 30) / 8 = 32.375 mpg
Median fuel efficiency = (30 + 31) / 2 = 30.5 mpg
Mode fuel efficiency = 35 mpg
For Car Company B:
Mean fuel efficiency = (29 + 33 + 36 + 27 + 34 + 34 + 34 + 25) / 8 = 31.5 mpg
Median fuel efficiency = (33 + 34) / 2 = 33.5 mpg
Mode fuel efficiency = 34 mpg
Based on the calculations:
1. The cars from both companies do not have the same mean, median, and mode, so the first statement is not true.
2. The cars from Company A do not have a higher median fuel efficiency than Company B, so the second statement is not true.
3. The cars from Company A do not have a higher mean fuel efficiency than Company B, so the third statement is not true.
4. The mode of fuel efficiency for Company B (34 mpg) is higher than the mode for Company A (35 mpg), so the fourth statement is true.
The correct statement is:
The cars from Company B have higher modal highway fuel efficiency than Company A.
For Car Company A:
Mean fuel efficiency = (35 + 28 + 35 + 30 + 31 + 38 + 35 + 30) / 8 = 32.375 mpg
Median fuel efficiency = (30 + 31) / 2 = 30.5 mpg
Mode fuel efficiency = 35 mpg
For Car Company B:
Mean fuel efficiency = (29 + 33 + 36 + 27 + 34 + 34 + 34 + 25) / 8 = 31.5 mpg
Median fuel efficiency = (33 + 34) / 2 = 33.5 mpg
Mode fuel efficiency = 34 mpg
Based on the calculations:
1. The cars from both companies do not have the same mean, median, and mode, so the first statement is not true.
2. The cars from Company A do not have a higher median fuel efficiency than Company B, so the second statement is not true.
3. The cars from Company A do not have a higher mean fuel efficiency than Company B, so the third statement is not true.
4. The mode of fuel efficiency for Company B (34 mpg) is higher than the mode for Company A (35 mpg), so the fourth statement is true.
The correct statement is:
The cars from Company B have higher modal highway fuel efficiency than Company A.