Use the table to answer the question.
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)
The mean time Group A spent shopping is minutes.
The mean time Group B spent shopping is minutes.
The mean times Group A and Group B spent shopping differ by minutes.
To find the mean time Group A spent shopping:
(18 + 20 + 46 + 34 + 58 + 31 + 41) / 7 = 248 / 7 = 35.4 minutes
So, the mean time Group A spent shopping is 35.4 minutes.
To find the mean time Group B spent shopping:
(15 + 21 + 32 + 42 + 29 + 57 + 39) / 7 = 235 / 7 = 33.6 minutes
So, the mean time Group B spent shopping is 33.6 minutes.
The difference in mean times Group A and Group B spent shopping is:
|35.4 - 33.6| = 1.8 minutes
Therefore, the mean times Group A and Group B spent shopping differ by 1.8 minutes.
Which data set has the highest median?(1 point)
Responses
{8, 20, 13, 14, 12, 9}
left brace 8 comma 20 comma 13 comma 14 comma 12 comma 9 right brace
{11, 15, 16, 8, 12, 14}
left brace 11 comma 15 comma 16 comma 8 comma 12 comma 14 right brace
{1, 10, 8, 29, 14, 17, 3}
left brace 1 comma 10 comma 8 comma 29 comma 14 comma 17 comma 3 right brace
{1, 6, 15, 7, 15, 18, 14}
To find the median of each data set, we first need to put the numbers in each set in order:
{8, 20, 13, 14, 12, 9} -> {8, 9, 12, 13, 14, 20}
The median is 13.
{11, 15, 16, 8, 12, 14} -> {8, 11, 12, 14, 15, 16}
The median is 13.
{1, 10, 8, 29, 14, 17, 3} -> {1, 3, 8, 10, 14, 17, 29}
The median is 10.
{1, 6, 15, 7, 15, 18, 14} -> {1, 6, 7, 14, 15, 15, 18}
The median is 14.
Therefore, the data set with the highest median is {1, 6, 15, 7, 15, 18, 14} with a median of 14.
Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most? (1 point)
Responses
Theo: 84, 88, 81, 85, 77, 76
Theo: 84, 88, 81, 85, 77, 76
Ara: 100, 98, 99, 97, 100, 100
Ara: 100, 98, 99, 97, 100, 100
Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82
Jose: 91, 93, 97, 96, 96, 96
To determine whose mean test score will increase the most, we first need to find the mean of their previous six test scores for each individual.
For Theo:
(84 + 88 + 81 + 85 + 77 + 76) / 6 = 491 / 6 = 81.8
For Ara:
(100 + 98 + 99 + 97 + 100 + 100) / 6 = 594 / 6 = 99
For Dana:
(68 + 74 + 83 + 80 + 81 + 82) / 6 = 468 / 6 = 78
For Jose:
(91 + 93 + 97 + 96 + 96 + 96) / 6 = 569 / 6 = 94.8
Now, let's calculate the difference between the recent perfect score of 100 and the previous mean score for each individual:
Theo: 100 - 81.8 = 18.2
Ara: 100 - 99 = 1
Dana: 100 - 78 = 22
Jose: 100 - 94.8 = 5.2
Therefore, Dana's mean test score will increase the most with a difference of 22 points.
The stem-and-leaf plot shows the speeds of the fastest steel roller coasters in Europe. The table shows the speeds of the fastest steel roller coasters in North America.
Speeds of the Fastest Steel Roller Coasters in Europe (in miles per hour)
Stem Leaf
7 4 5 5 5
8 0 0 3 4 8
9 9
11 1
Key: 7|4=74 miles per hour
Speeds of the Fastest Steel Roller Coasters in North America (in miles per hour)
Canada 90 128 91
U.S. 93 120 100
Mexico 95 92 85
Find the range of the speeds of the fastest steel roller coasters on both continents.
(1 point)
The range of the speeds of the fastest steel roller coasters in Europe is mph. The range of the speeds of the fastest steel roller coasters in North America is mph.
To find the range of the speeds of the fastest steel roller coasters on both continents:
For Europe:
The minimum speed is 74 mph and the maximum speed is 118 mph.
Range = Maximum speed - Minimum speed
Range = 118 - 74
Range = 44 mph
For North America:
The minimum speed is 85 mph and the maximum speed is 128 mph.
Range = Maximum speed - Minimum speed
Range = 128 - 85
Range = 43 mph
Therefore, the range of the speeds of the fastest steel roller coasters in Europe is 44 mph, and the range of the speeds of the fastest steel roller coasters in North America is 43 mph.
Anthony wants to know the average daily high temperatures in his town during the summer. He chose two random samples of 10 consecutive days and recorded the daily high temperatures. The daily high temperatures in Fahrenheit are as follows.
Sample 1: 78 82 85 87 90 85 79 86 91 88
Sample 2: 81 79 80 86 89 92 82 88 84 87
Find the mean daily high temperatures of each sample and calculate the difference between these mean daily high temperatures.
(2 points)
The mean daily high temperature of Sample 1 is °.
The mean daily high temperature of Sample 2 is °.
The mean daily high temperatures of the two samples differ by °
To find the mean daily high temperature of each sample:
For Sample 1:
(78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88) / 10 = 851 / 10 = 85.1 degrees Fahrenheit
For Sample 2:
(81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87) / 10 = 848 / 10 = 84.8 degrees Fahrenheit
Now, calculate the difference between the mean daily high temperatures of the two samples:
|85.1 - 84.8| = 0.3 degrees
Therefore, the mean daily high temperature of Sample 1 is 85.1 degrees, the mean daily high temperature of Sample 2 is 84.8 degrees, and the mean daily high temperatures of the two samples differ by 0.3 degrees Fahrenheit.
These are the scores for two randomly selected lacrosse teams. Find the range of the number of goals scored by each team. Based on the range, which team has a more consistent number of goals scored?
Lacrosse Team 1: 6 0 4 17 3 12
Lacrosse Team 2: 23 14 22 14 17 22
(2 points)
The range of the number of goals scored by Lacrosse Team 1 is . The range of the number of goals scored by Lacrosse Team 2 is . Based on the range, Lacrosse Team has a more consistent number of goals scored.