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.
Class 1 has a higher median than Class 2 by 0.5 mile.
Comparing Data Distributions Quick Check
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Question
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 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 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 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.
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The mean time taken by Group A is higher than that of Group B 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 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.
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.
Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
To find the medians of the two classes, let's first arrange the data in ascending order:
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
Now, let's find the median of each class:
For Class 1, the number of data points is odd, so the median is the middle value, which is 8.
For Class 2, the number of data points is also odd, so the median is the middle value, which is 7.
The difference between the medians is 8 - 7 = 1 mile.
Therefore, Class 1 has a higher median than Class 2 by 1 mile.
To find the difference between the medians of the two classes and determine which class has a higher median, follow these steps:
1. First, sort the data for each class in ascending order:
Class 1: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14
Class 2: 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12
2. Next, calculate the medians for each class:
- Class 1 has 15 data points, so the median is the average of the 8th and 9th values: (8 + 8) / 2 = 8
- Class 2 also has 15 data points, so the median is the average of the 7th and 8th values: (7 + 7) / 2 = 7
3. The difference between the medians is: 8 - 7 = 1 mile.
4. Since Class 1 has a median of 8 and Class 2 has a median of 7, Class 1 has a higher median.
Therefore, the correct response is:
Class 1 has a higher median than Class 2 by 1 mile.