Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers.
Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}
Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}
Which statement is true for the data sets?
A.
The mean study time of students in Class A is less than students in Class B.
B.
The mean study time of students in Class B is less than students in Class A.
C.
The median study time of students in Class B is greater than students in Class A.
D.
The range of study time of students in Class A is less than students in Class B.
E.
The mean and median study time of students in Class A and Class B is equal
To find the mean study time, we need to add up all the values in each dataset and then divide by the total number of values.
For Class A:
Mean study time = (2 + 5 + 7 + 6 + 4 + 3 + 8 + 7 + 4 + 5 + 7 + 6 + 3 + 5 + 4 + 2 + 4 + 6 + 3 + 5) / 20 = 4.65
For Class B:
Mean study time = (3 + 7 + 6 + 4 + 3 + 2 + 4 + 5 + 6 + 7 + 2 + 2 + 2 + 3 + 4 + 5 + 2 + 2 + 5 + 6) / 20 = 4.05
Therefore, the statement "The mean study time of students in Class A is less than students in Class B" is FALSE.
To find the median study time, we need to arrange all the values in each dataset in order and find the middle value.
For Class A:
Arranged dataset: {2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8}
Median study time = (5 + 5) / 2 = 5
For Class B:
Arranged dataset: {2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7}
Median study time = 4
Therefore, the statement "The median study time of students in Class B is greater than students in Class A" is FALSE.
To find the range of study time, we need to subtract the minimum value from the maximum value in each dataset.
For Class A:
Range = 8 - 2 = 6
For Class B:
Range = 7 - 2 = 5
Therefore, the statement "The range of study time of students in Class A is less than students in Class B" is FALSE.
Finally, since the mean and median study time for both classes are not equal, the statement "The mean and median study time of students in Class A and Class B is equal" is FALSE.
In conclusion, the correct statement is:
E. The mean and median study time of students in Class A and Class B is not equal.