select the correct answer. twenty students in class a and 20 students in class b were asked how many hours…

Explanation:

Step1: Calculate mean of Class A

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 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 mean of Class B, $\bar{x}_B=\frac{80}{20}=4$.

Step3: Analyze median of Class A

Arrange Class A data in ascending - order: ${2,2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8}$. Since $n = 20$ (even), median is the average of the 10th and 11th ordered values. Median of Class A, $M_A=\frac{5 + 5}{2}=5$.

Step4: Analyze median of Class B

Arrange Class B data in ascending - order: ${2,2,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7}$. Since $n = 20$ (even), median is the average of the 10th and 11th ordered values. Median of Class B, $M_B=\frac{4+4}{2}=4$.

Step5: Analyze range of Class A

Range formula is $R=\text{Max}-\text{Min}$. For Class A, $\text{Max}=8$, $\text{Min}=2$, so $R_A=8 - 2=6$.

Step6: Analyze range of Class B

For Class B, $\text{Max}=7$, $\text{Min}=2$, so $R_B=7 - 2=5$.

Answer:

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