Enables to find the arithmetic mean and also to find the weighted mean of the observations 42, 13, 3, 85, 14, 25, 38, 23, 45, 52.

$$\sum (x_i \cdot w_i) = (50 \times 4) + (65 \times 2) + (75 \times 1) + (53 \times 3) + (58 \times 3)$$ $$\sum (x_i \cdot w_i) = 200 + 130 + 75 + 159 + 174$$ $$\sum (x_i \cdot w_i) = 738$$

$$\sum w_i = 4 + 2 + 1 + 3 + 3$$ $$\sum w_i = 13$$

The formula for the weighted arithmetic mean is $\bar{x}_w = \frac{\sum (x_i \cdot w_i)}{\sum w_i}$.

$$\bar{x}_w = \frac{738}{13}$$ $$\bar{x}_w \approx 56.77$$

$$\sum x_i = 50 + 65 + 75 + 53 + 58$$ $$\sum x_i = 301$$

The number of subjects ($n$) is 5. The formula for the simple arithmetic mean is $\bar{x} = \frac{\sum x_i}{n}$.

$$\bar{x} = \frac{301}{5}$$ $$\bar{x} = 60.2$$

The weighted arithmetic mean (the grade) is approximately 56.77, and the simple arithmetic mean is 60.2.

The grade (weighted arithmetic mean) is: $\boxed{\text{56.77}}$
The arithmetic mean is: $\boxed{\text{60.2}}$