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.
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.
Small dogs, because the range of their weights is greater than that of cats.
Small dogs, because the range of their weights is less than that of cats.
This is evident as the dot plot for small dogs has a narrower spread of weights compared to the dot plot for cats.
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
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
0.13 pounds
1 pound
The modal weight for cats is 11 pounds (4 dots above 11), and the modal weight for small dogs is also 11 pounds (4 dots above 10).
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 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.
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 2 has a higher median than Class 1 by 1 mile.
Class 2 has a higher median than Class 1 by 1 mile.
Class 1 has a higher median than Class 2 by 1 mile.
To find the medians for each class, we first need to arrange the data in ascending order:
For Class 1: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
For Class 2: 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 12
Median for Class 1: (8 + 10) / 2 = 9
Median for Class 2: (7 + 8) / 2 = 7.5
The difference between the medians is 9 - 7.5 = 1.5 miles.
Since 9 is the median for Class 1 and 7.5 is the median for Class 2, Class 1 has a higher median by 1.5 miles.
Therefore, the correct response is:
Class 1 has a higher median than Class 2 by 1.5 miles.
The data shows the number of seconds it took two randomly selected groups to thread a needle. Compare the measures of center and variability of these data sets.
Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Which of the following statements about these data sets is false?
(1 point)
Responses
The mean time taken by Group A is higher than that of Group B.
The mean time taken by Group A is higher than that of Group B.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
The ranges of the time taken by Group A and Group B are the same.
The ranges of the time taken by Group A and Group B are the same.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
The statement "The ranges of the time taken by Group A and Group B are the same" is false.
To determine the measures of center and variability for each group:
Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Mean (Group A): (56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10) / 10 = 29.3
Median (Group A): 28.5
Range (Group A): 80 - 3 = 77
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Mean (Group B): (27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20) / 10 = 16.7
Median (Group B): 18.5
Range (Group B): 27 - 5 = 22
From the calculations, we can see that the range of the time taken by Group A (77) is different from the range of the time taken by Group B (22). This means that the statement "The ranges of the time taken by Group A and Group B are the same" is false.
Two fertilizers are applied to randomly selected potato plants. After several weeks, the potatoes are weighed. The weights in kilograms are as follows. Which fertilizer is generally more effective?
Fertilizer A: 27, 20, 16, 18, 22, 19, 23, 21, 17, 19
Fertilizer B: 28, 19, 18, 21, 24, 20, 25, 27, 29, 21
(1 point)
Responses
Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher.
Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher.
Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
To determine which fertilizer is generally more effective, we can compare the mean and median weights of the potatoes treated with each fertilizer.
Calculations:
For Fertilizer A:
Mean weight = (27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19) / 10 = 20.2
Median weight = 19.5
For Fertilizer B:
Mean weight = (28 + 19 + 18 + 21 + 24 + 20 + 25 + 27 + 29 + 21) / 10 = 22.2
Median weight = 21
Comparing the mean and median weights:
- Fertilizer A: Mean = 20.2; Median = 19.5
- Fertilizer B: Mean = 22.2; Median = 21
Based on the mean and median weights, Fertilizer B is generally more effective as both the mean and median weights of the potatoes treated with it are higher than those treated with Fertilizer A. This indicates that Fertilizer B leads to higher average and middle values of the weights of the potato plants, suggesting it may be more effective.
Therefore, the correct response is: Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.