Comparing Data Distributions Quick Check
1 of 51 of 5 Items
Question
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 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.
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.
Comparing Data Distributions Quick Check
2 of 52 of 5 Items
Question
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
3 pounds
3 pounds
The modal weights are the same for cats and small dogs.
The modal weights are the same for cats and small dogs.
1 pound
1 pound
0.13 pounds
3 pounds
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 0.5 mile.
Class 1 has a higher median than Class 2 by 0.5 mile.
Class 1 has a higher median than Class 2 by 1 mile.
To find the median, we need to arrange the data in order from least to greatest:
Class 1: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
Class 2: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
The median of Class 1 is the middle value, which is 8.
The median of Class 2 is also the middle value, which is 7.
Therefore, Class 1 has a higher median than Class 2 by 1 mile.
The correct response is:
Class 1 has a higher median than Class 2 by 1 mile.
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 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 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 mean time taken by Group A is higher than that of Group B.
To compare the measures of center and variability of the data sets, let's calculate the medians and ranges for both groups:
Group A (in seconds): 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
Median of Group A: (sorted data) 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
Median of Group A: 28
Group B (in seconds): 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
Median of Group B: (sorted data) 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
Median of Group B: 18
Range of Group A: 80 - 3 = 77
Range of Group B: 27 - 5 = 22
Now let's evaluate the statements:
1. The median time taken by members of Group A to thread a needle is higher than that of members of Group B. - True (28 > 18)
2. 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. - True (77 > 22)
3. The ranges of the time taken by Group A and Group B are the same. - False (ranges are different)
4. The mean time taken by Group A is higher than that of Group B. - We don't have the means, so we can't determine if this statement is true or false.
Therefore, the false statement is:
The ranges of the time taken by Group A and Group B are the same.
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 both ineffective, because there is no difference in the ranges of the weights of the potatoes.
Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
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.
To determine which fertilizer is generally more effective, let's compare the measures of center (mean and median) for both groups and also consider the ranges of the weights:
Fertilizer A (in kilograms): 16, 17, 18, 19, 19, 20, 21, 22, 23, 27
Mean of Fertilizer A: (sum of weights) 222 / (number of potatoes) 10
Mean of Fertilizer A: 22.2
Median of Fertilizer A: (sorted weights) 16, 17, 18, 19, 19, 20, 21, 22, 23, 27
Median of Fertilizer A: 20
Range of Fertilizer A: 27 - 16 = 11
Fertilizer B (in kilograms): 18, 19, 20, 21, 21, 24, 25, 27, 28, 29
Mean of Fertilizer B: (sum of weights) 232 / (number of potatoes) 10
Mean of Fertilizer B: 23.2
Median of Fertilizer B: (sorted weights) 18, 19, 20, 21, 21, 24, 25, 27, 28, 29
Median of Fertilizer B: 21
Range of Fertilizer B: 29 - 18 = 11
Now, let's evaluate the statements:
1. Fertilizers A and B are both ineffective because there is no difference in the ranges of the weights of the potatoes. - False (ranges are the same for both)
2. Fertilizers A and B are equally effective because the ranges of the weights of the potatoes are the same. - False (ranges are the same, but we need to consider other measures)
3. Fertilizer B is generally more effective because the mean and median weights of the potatoes that were treated with it are higher. - True (mean and median are higher for Fertilizer B)
4. Fertilizer A is generally more effective because the mean and median weights of the potatoes treated with it are higher. - False (mean and median are higher for Fertilizer B)
Therefore, the correct statement is:
Fertilizer B is generally more effective because the mean and median weights of the potatoes that were treated with it are higher.