Calculate the missing frequencies for the given particle size ranges using the provided fX and Mean (X) values.

In the provided table, the "fX" column is calculated by multiplying the "Mean (X)" by the "Freq (f)".
The formula is:

$$fX = \text{Mean (X)} \times \text{Freq (f)}$$

To find the frequency (Freq (f)), divide the "fX" value by the "Mean (X)" value:

$$\text{Freq (f)} = \frac{fX}{\text{Mean (X)}}$$

For the particle size range 41-50:
Given: Mean (X) = 45, fX = 887.5
Substitute these values into the formula:

$$\text{Freq (f)} = \frac{887.5}{45}$$ $$\text{Freq (f)} \approx 19.722$$

Rounding to two decimal places, the frequency is:

$$\boxed{\text{Freq (f)} \approx \mathbf{19.72}}$$

For the particle size range 51-60:
Given: Mean (X) = 55, fX = 682.5
Substitute these values into the formula:

$$\text{Freq (f)} = \frac{682.5}{55}$$ $$\text{Freq (f)} \approx 12.409$$

Rounding to two decimal places, the frequency is:

$$\boxed{\text{Freq (f)} \approx \mathbf{12.41}}$$