Question

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)

A. Class 2 has a higher median than Class 1 by 1 mile.
B. Class 1 has a higher median than Class 2 by 0.5 mile.
C. Class 2 has a higher median than Class 1 by 0.5 mile.
D. Class 1 has a higher median than Class 2 by 1 mile.

Answer 1

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)

A. The ranges of the time taken by Group A and Group B are the same.
B. The mean time taken by Group A is higher than that of Group B.
C. The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
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.

Answer 2

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)

A. Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.
B. Fertilizers A and B are both ineffective, because there is no difference in the ranges of the weights of the potatoes.
C. Fertilizer A is generally more effective, because the mean and median weights of the potatoes treated with it are higher.
D. Fertilizers A and B are equally effective, because the ranges of the weights of the potatoes are the same.

Answer 3

First, we need to find the medians of both classes:

Class 1: 2, 4, 5, 5, 6, 7, 7, 8, 8, 10, 10, 11, 11, 12, 14 (arranged in order)

Median = 8

Class 2: 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12 (arranged in order)

Median = 7

The difference between the medians is 8 - 7 = 1. Therefore, Class 1 has a higher median than Class 2 by 1 mile.

The answer is D. Class 1 has a higher median than Class 2 by 1 mile.

Answer 4

A. The ranges of the time taken by Group A and Group B are the same.

This statement is false. We can calculate the range of each data set by subtracting the minimum value from the maximum value:

Range of Group A: 80 - 3 = 77 seconds
Range of Group B: 27 - 5 = 22 seconds

Therefore, the range of the time taken by Group A is higher than that of Group B.

The answer is A.

Answer 5

To determine which fertilizer is generally more effective, we need to compare the measures of center and variability for both data sets.

Fertilizer A: Mean = 20.2, Median = 19, Range = 11
Fertilizer B: Mean = 22.2, Median = 21, Range = 11

Fertilizer B has a slightly higher mean and median weight for the potatoes, and both data sets have the same range. Therefore, we can conclude that Fertilizer B is generally more effective.

The answer is A. Fertilizer B is generally more effective, because the mean and median weights of the potatoes that were treated with it are higher.