Weight in pounds - Cats
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.
. . .
.____.__.___.____._
| | | | |
9 10 11 12 13
Weight in pounds - Small Dogs
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.
. . . . .
._____._____._____.____._____.____._____.__
| | | | | | | |
8 9 10 11 12 13 14 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?
a. 0.13 pounds
b. the modal weights are the same for cats and small dogs.
c. 3 pounds
d. 1 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
a. class 2 has a higher median than class 1 by 0.5 mile.
b. class 1 has higher median than class 2 by 1 mile.
c. class 2 has a higher median than class 1 by 1 mile.
d. class 1 has higher median than class 2 by 0.5 mile.
To find the median, we first need to arrange the data in 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
For Class 1, there are 15 data points, so the median is the middle value:
Median for Class 1 = 8
For Class 2, there are also 15 data points, so the median is the average of the two middle values:
Median for Class 2 = (7 + 8) / 2 = 7.5
The difference between the medians is:
8 - 7.5 = 0.5
So,
a. class 1 has higher median than class 2 by 0.5 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?
A. The mean time taken by Group A is higher than that of Group B.
B. The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
C. The ranges of the time taken by Group A and Group B are the same.
D. 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.
To compare the measures of center and variability:
For Student Group A:
Mean = (56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10) / 10 = 30.3
Median = 28
Range = 80 - 3 = 77
Variance = 439.36
Standard Deviation = 20.96
For Student Group B:
Mean = (27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20) / 10 = 17.7
Median = (18 + 19) / 2 = 18.5
Range = 27 - 5 = 22
Variance = 61.19
Standard Deviation = 7.82
Based on the calculations:
A. The mean time taken by Group A is higher than that of Group B. - True
B. The median time taken by members of Group A to thread a needle is higher than that of members of Group B. - False
C. The ranges of the time taken by Group A and Group B are the same. - False
D. 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
Therefore, the false statement is:
B. The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
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
A. Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
B. Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
C. Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
D. 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, we need to compare the measures of center (mean and median) and variability (range) for the weights of the potatoes:
For Fertilizer A:
Mean = (27 + 20 + 16 + 18 + 22 + 19 + 23 + 21 + 17 + 19) / 10 = 20.2
Median = 19
Range = 27 - 16 = 11
For Fertilizer B:
Mean = (28 + 19 + 18 + 21 + 24 + 20 + 25 + 27 + 29 + 21) / 10 = 22.2
Median = 21
Range = 29 - 18 = 11
Based on the calculations:
A. Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes. - This statement is incorrect as it does not consider all factors.
B. Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher. - This statement is not entirely accurate as the median is the same for both fertilizers.
C. Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same. - This statement is correct based on the range.
D. Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher. - This statement is incorrect as the mean and median for Fertilizer B are actually higher.
Therefore, the correct statement is:
C. Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.
c. 3 pounds
The mode for cats is 12 pounds, while the mode for small dogs is 15 pounds. The difference between the two modes is 3 pounds.