# [ASK] Is Expected Frequency Rounded Up or Down?

#### Monoxdifly

A die is tossed 100 times. What's the expected frequency that the number appears will be 4?

The probability is 1/6, so the expected frequency is 1/6 × 100, but that results in a fraction (16 2/3). Do we need to round it up or down? Is the answer 16 or 17?

#### romsek

MHF Helper
You don't need to round it at all. The correct answer is $\dfrac{50}{3}$

True you won't see 2/3 of a die but that doesn't matter. An expectation is an average and as such there's no reason to expect it must be an integer.

#### Monoxdifly

Okay then, thanks.

#### TKHunny

If you are forced to round, for whatever reason, you will need to decide exactly how to do that.

Typically, a simple up or down methodology will prove unsatisfactory as you will violate the definition of a probability distribution:

Down 2 dp
1/3 = 0.33
1/3 = 0.33
1/3 = 0.33
0.33 * 3 = 0.99 and that is NOT 1.00

Likewise, fudging (forced footing) proves unsatisfactory:

1/3 = 0.33
1/3 = 0.33
1/3 = 0.34

They are not really equal, are they.

Unless you are in a purely theoretical pursuit, you just have to make up your mind what is and is not suitable.

#### Monoxdifly

Oh well, no rounding then, thanks.