Question

select the correct answer.
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.

Explanation:

Step1: Calculate mean of Class A

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For Class A, $n = 20$, and $\sum_{i=1}^{20}x_{i}=2 + 5+7 + 6+4 + 3+8+7+4+5+7+6+3+5+4+2+4+6+3+5=100$. So the mean of Class A, $\bar{x}_A=\frac{100}{20}=5$.

Step2: Calculate mean of Class B

For Class B, $n = 20$, and $\sum_{i = 1}^{20}x_{i}=3+7+6+4+3+2+4+5+6+7+2+2+2+3+4+5+2+2+5+6 = 80$. So the mean of Class B, $\bar{x}_B=\frac{80}{20}=4$.

Step3: Analyze the statements

Since $\bar{x}_A = 5$ and $\bar{x}_B=4$, the mean study - time of students in Class B is less than students in Class A.

Answer:

B. The mean study time of students in Class B is less than students in Class A.