Question

two class 6 students have two different classes (the number of hours they spend during homework each night).
class 1: 1.20, 1.30, 1.30, 2.10, 2.15, 4.25
class 2: 1.50, 1.40, 0.75, 3.10, 2.10, 2.00
which statement is true?
a the mean and median for class 1 are higher than those for class 2.
b the mean and median for class 2 are higher than those for class 1.
c the mean for class 1 is higher, but the median for class 2 is higher.
d the mean for class 2 is higher, but the median for class 1 is higher.

Explanation:

Step1: Calculate the mean for Class 1

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For Class 1: $n = 6$, $x=\{1.20,1.50,1.70,2.10,2.15,4.15\}$.
$\sum_{i=1}^{6}x_{i}=1.20 + 1.50+1.70 + 2.10+2.15+4.15=12.8$.
$\bar{x}_{1}=\frac{12.8}{6}\approx2.13$.

Step2: Calculate the median for Class 1

Arrange the data in ascending order: $1.20,1.50,1.70,2.10,2.15,4.15$.
Since $n = 6$ (even), the median $M_{1}=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}=\frac{1.70 + 2.10}{2}=1.90$.

Step3: Calculate the mean for Class 2

For Class 2: $n = 6$, $x=\{1.50,1.60,1.75,3.10,3.15,3.60\}$.
$\sum_{i = 1}^{6}x_{i}=1.50+1.60 + 1.75+3.10+3.15+3.60=14.7$.
$\bar{x}_{2}=\frac{14.7}{6}=2.45$.

Step4: Calculate the median for Class 2

Arrange the data in ascending order: $1.50,1.60,1.75,3.10,3.15,3.60$.
Since $n = 6$ (even), the median $M_{2}=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}=\frac{1.75+3.10}{2}=2.425$.

Answer:

D. The mean for class 2 is higher, but the median for class 1 is higher.