The points scored by a football team are 17, 23, 15, 21, 7, and 13. What is the range?
To find the percentage of the total polled residents who would vote for Candidate A, we need to add up the number of votes for Candidate A in both samples and divide by the total number of residents polled:
Total number of votes for Candidate A = 346 + 248 = 594
Total number of residents polled = 500 + 500 = 1000
Percentage of residents who would vote for Candidate A = (594/1000) x 100% = 59.4%
Therefore, 59.4% of the total polled residents would vote for Candidate A as the town mayor.
The range is the difference between the highest and lowest values in the set. In this case, the highest value is 23 and the lowest value is 7, so:
Range = 23 - 7 = 16
Therefore, the range of the points scored by the football team is 16.
A poll is conducted to determine who is most likely to win the election for town mayor. Two random samples of 500 residents each are polled. The data is as follows.
Candidate A Candidate B Total
Sample 1 346 154 500
Sample 2 248 252 500
What percentage of the total polled residents would vote for Candidate A as the town mayor?
To determine the average height of trees in a national forest, 10 trees are randomly selected. Their heights in feet are 85.4, 87.6, 87.1, 85.6, 85.9, 85.3, 84.9, 83.7, 84.0, and 85.2. To ensure the accuracy of the data, another set of 10 trees is randomly selected. Their heights are 87.1, 88.0, 84.2, 85.3, 86.5, 84.2, 83.2, 84.1, 85.2, and 87.3. What is the difference between the mean heights of the trees of these two random samples?
Here are the math quiz scores for Student 1 and Student 2.
Student 1: 75 80 84 79 92 86 88 86 86 90
Student 2: 83 85 91 93 72 85 76 80 82 89
Find the range of each student’s math quiz scores. Based on the range, which student performed more consistently on their math quizzes?
(2 points)
The range of Student 1’s math quiz scores is
. The range of Student 2’s math quiz scores is
. Based on the range, Student
performed more consistently on the math quizzes.
The range of Student 1’s math quiz scores is the difference between the highest score and the lowest score. Therefore:
Range of Student 1 = 92 - 75 = 17
The range of Student 2’s math quiz scores is:
Range of Student 2 = 93 - 72 = 21
Based on the range, Student 1 performed more consistently on their math quizzes because their scores were more closely grouped together. Student 1's scores ranged from 75 to 92, with a difference of only 17 points between the highest and lowest score, while Student 2's scores ranged from 72 to 93, with a difference of 21 points between the highest and lowest score.
The numbers of miles Ron biked are 31, 35, 49, 32, 45, 29, 33, 28, and 40.
Determine the range of this data set.(1 point)
The range of a data set is the difference between the highest and lowest values.
In this case, the highest value is 49 and the lowest value is 28. Therefore,
Range = 49 - 28 = 21
The range of the data set is 21.
Which of the following data sets has the smallest range?(1 point)
Responses
{324, 318, 367, 312, 389, 337}
left brace 324, 318, 367, 312, 389, 337 right brace
{37, 19, 40, 54, 75, 68}
left brace 37, 19, 40, 54, 75, 68 right brace
{50, 30, 10, 0, 80, 100}
left brace 50, 30, 10, 0, 80, 100 right brace
{148, 145, 117, 148, 199, 172}
left brace 148, 145, 117, 148, 199, 172 right brace
The range of a data set is the difference between the highest and lowest values.
The range of each data set is:
- Range of {324, 318, 367, 312, 389, 337} = 389 - 312 = 77
- Range of {37, 19, 40, 54, 75, 68} = 75 - 19 = 56
- Range of {50, 30, 10, 0, 80, 100} = 100 - 0 = 100
- Range of {148, 145, 117, 148, 199, 172} = 199 - 117 = 82
Therefore, the data set with the smallest range is {37, 19, 40, 54, 75, 68}.
The data from two random samples of 200 people regarding their favorite nuts is shown in the following table.
Almond Pistachio Cashew Walnuts Total
Sample 1 40 62 63 35 200
Sample 2 43 64 61 32 200
Based on the two samples, what percentage of the people prefer cashew nuts?
(1 point)
To find the percentage of people who prefer cashew nuts, we need to add up the number of people who prefer cashews in both samples and divide by the total number of people sampled:
Total number of people who prefer cashews = 63 + 61 = 124
Total number of people sampled = 200 + 200 = 400
Percentage of people who prefer cashew nuts = (124/400) x 100% = 31%
Therefore, based on the two samples, 31% of the people prefer cashew nuts.
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 more 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
(1 point)
Responses
Cars from both companies have equally consistent highway fuel efficiency.
Cars from both companies have equally consistent highway fuel efficiency.
Car Company A is more consistent, because the range of highway fuel efficiency of its cars is higher than that of Car Company B.
Car Company A is more consistent, because the range of highway fuel efficiency of its cars is higher than that of Car Company B.
Car Company B is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company A.
Car Company B is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company 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 is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B.
The range of a data set is the difference between the highest and lowest values. A smaller range indicates that the values in the set are closer together, which means the set is more consistent.
Car Company A: Range = 36 - 28 = 8
Car Company B: Range = 40 - 25 = 15
Since Car Company A has a smaller range, which means that the values are closer together, it is more consistent in highway fuel efficiency than Car Company B. Therefore, the correct answer is "Car Company A is more consistent, because the range of highway fuel efficiency of its cars is lower than that of Car Company B."
The randomly selected delivery times, in minutes, of two restaurants are as follows. Which restaurant has more consistent delivery times?
Restaurant 1 Restaurant 2
40 42
37 38
40 37
41 39
38 38
46 40
41 42
37 41
40 40(1 point)
Responses
Restaurant 2 is more consistent, because the range of its delivery times is lower than that of Restaurant 1.
Restaurant 2 is more consistent, because the range of its delivery times is lower than that of Restaurant 1.
Restaurant 1 is more consistent, because the range of its delivery times is lower than that of Restaurant 2.
Restaurant 1 is more consistent, because the range of its delivery times is lower than that of Restaurant 2.
Restaurant 2 is more consistent, because the range of its delivery times is higher than that of Restaurant 1.
Restaurant 2 is more consistent, because the range of its delivery times is higher than that of Restaurant 1.
The delivery times of both restaurants are equally consistent.
The delivery times of both restaurants are equally consistent.
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The range of a data set is the difference between the highest and lowest values. A smaller range indicates that the values in the set are closer together, which means the set is more consistent.
Restaurant 1: Range = 46 - 37 = 9
Restaurant 2: Range = 42 - 37 = 5
Since Restaurant 2 has a smaller range, which means that the values are closer together, it is more consistent in delivery times than Restaurant 1. Therefore, the correct answer is "Restaurant 2 is more consistent, because the range of its delivery times is lower than that of Restaurant 1."
Ten randomly selected people were asked to join a fitness group. Over the next two weeks, they were tested on how many push-ups they could do. The data shows the number of push-ups they did over the two weeks. From the first to the second week, what was the increase in the median number of push-ups?
Week 1: 5, 8, 10, 11, 6, 8, 9, 15, 5, 8
Week 2: 7, 9, 11, 12, 8, 10, 11, 18, 9, 10
(1 point)
To find the increase in the median number of push-ups from the first week to the second week, we need to find the median of each week's data set and then subtract the median of the first week from the median of the second week.
To find the median, we need to put the data sets in order from least to greatest:
Week 1: 5, 5, 6, 8, 8, 8, 9, 10, 11, 15
Week 2: 7, 8, 9, 10, 11, 11, 12, 18
The median of the first week's data set is the average of the two middle numbers: (8 + 8)/2 = 8
The median of the second week's data set is the middle number: 11
The increase in the median number of push-ups from the first week to the second week is:
11 - 8 = 3
Therefore, the increase in the median number of push-ups is 3.
Use the image to answer the question.
An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13. For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.
The dot plots show the weights of randomly selected cats and small dogs in different households. Based on an informal assessment of the visual overlap of these distributions, which animal has the least variability in their weights? Why?
(1 point)
Responses
Small dogs, because the range of their weights is less than that of cats.
Small dogs, because the range of their weights is less than that of cats.
Small dogs, because the range of their weights is greater than that of cats.
Small dogs, because the range of their weights is greater than that of cats.
Cats, because the range of their weights is less than that of small dogs.
Cats, because the range of their weights is less than that of small dogs.
Cats, because the range of their weights is greater than that of small dogs.
Cats, because the range of their weights is greater than that of small dogs.
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Variability refers to how much the data values are spread out or dispersed. One way to assess the variability of the data is to look at the range, which is the difference between the maximum and minimum values in the data set. A smaller range indicates less variability, while a larger range indicates more variability.
Looking at the dot plots for cats and small dogs, we can see that the range of weights for small dogs is greater than the range of weights for cats. Small dogs have weights ranging from 8 to 15 pounds, while cats have weights ranging from 9 to 13 pounds. This means that small dogs have more variability in their weights, while cats have less variability.
Therefore, the correct answer is "Cats, because the range of their weights is less than that of small dogs."
Use the image to answer the question.
An illustration shows two sets of dot plots. One is titled Weight in Pounds, Cats and the other is Weight in Pounds, Small Dogs. The plots are shown as an abacus-like representation with dots in a vertical row over each number on a number line. For Cats, a number line with arrows on both ends ranges from 9 to 13 in increments of 1. There is 1 dot above 9, 2 dots above 10, 4 dots above 11, 2 dots above 12, and one dot above 13. For Small Dogs, a number line with arrows on both ends ranges from 8 to 15 in increments of 1. There is 1 dot above 8, 2 dots above 9, 4 dots above 10, 2 dots above 11, 2 dots above 12, 2 dots above 13, 1 dot above 14, and 1 dot above 15.
The dot plots show the weights of randomly selected cats and small dogs in different households. What is the difference between the modal weights of cats and small dogs?
(1 point)
Responses
0.13 pounds
0.13 pounds
The modal weights are the same for cats and small dogs.
The modal weights are the same for cats and small dogs.
3 pounds
3 pounds
1 pound
1 pound
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The modal weight is the weight that occurs most frequently in the data, which is represented by the highest dot in the dot plot.
Looking at the dot plots for cats and small dogs, we see that the modal weight for cats is 11 pounds and the modal weight for small dogs is 10 pounds.
The difference between these modal weights is:
11 - 10 = 1
Therefore, the difference between the modal weights of cats and small dogs is 1 pound.
The data shows the number of miles run per week by randomly selected students from two different classes. Find the difference between the medians. Which class has a higher median? By how much?
Class 1: 6, 8, 10, 11, 14, 4, 5, 8, 2, 7, 7, 5, 10, 12, 11
Class 2: 6, 4, 5, 6, 7, 8, 12, 9, 10, 11, 5, 8, 7, 4, 10
(1 point)
Responses
Class 2 has a higher median than Class 1 by 1 mile.
Class 2 has a higher median than Class 1 by 1 mile.
Class 2 has a higher median than Class 1 by 0.5 mile.
Class 2 has a higher median than Class 1 by 0.5 mile.
Class 1 has a higher median than Class 2 by 1 mile.
Class 1 has a higher median than Class 2 by 1 mile.
Class 1 has a higher median than Class 2 by 0.5 mile.
Class 1 has a higher median than Class 2 by 0.5 mile.
To find the mean height of the trees in each sample, we need to add up all of the heights and divide by the number of trees:
Mean height of first sample = (85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2)/10 = 85.38 ft
Mean height of second sample = (87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3)/10 = 85.91 ft
The difference between the means is:
85.91 - 85.38 = 0.53
Therefore, the difference between the mean heights of the two random samples is 0.53 feet.