How to round mean values when imputing missing questionnaire items When there are missing items (answers) in a questionnaire it is sometimes usual to impute them with the mean of the valid items. For example here are 3 items/question which can have a four values from 1 to including 4.

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*[2, 3, missing] would result in [2, 3, 2.5]

*[4, 3, missing] would result in [2, 3, 3.5]
Because the floating point is not a valid/possible answer, rounding may be needed to give the item one of the allowed values.
Is scientific rounding the correct choice here? Please correct me if I am wrong but possible synonyms are symmetric rounding, mathematics rounding, round half down or bankers rounding.
In that case and if I am interpreting the rounding rule correct:

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*[2, 3, missing] would result in [2, 3, 2]

*[4, 3, missing] would result in [2, 3, 3]
This question does not take technical problems (e.g. representation of floating point numbers) into account. This is about the best theoretical choice and not how to implement it.
More thoughts
Assume the case of a questionnaire where I have 3 to 5 items with possible values between 1 and 4. The calculation of mean() will often result in a *.5 number. Using scientific rounding will round them all down. I would hypothesize that more then the half of the rounding will go down which causes an unbalance.
Because of that I would argue that rounding to the nearest even value would result in a better balance between up and down rounding.
What does the more experience researches thing about that?
EDIT: This question is not about the right imputation method. The questionnaire author said I have to use this method not other. The question is about the rounding method only.

It's commonly done to impute based on the mean of the other items, but that's more because it's simple, easy to do and has some vague logic to it ("Well, if they are all high or low, maybe the missing one would be, too, right?"). However, that does not mean it is a good (never mind the best) option.
Let's imagine you have this data for one person:

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*Week 0, Question 1: Score 9 out of 10

*Week 0, Question 2: Score 8 out of 10

*Week 0, Question 3: Score 2 out of 10

*Week 4, Question 1: Score 8 out of 10

*Week 4, Question 2: Score 9 out of 10

*Week 4, Question 3: Score 1 out of 10

*Week 8, Question 1: Score 10 out of 10

*Week 8, Question 2: Score 9 out of 10

*Week 8, Question 3: missing

Would your first thought be to impute question 3 at week at as 9.5?
A more obvious approach is to e.g. do multiple imputation based on a joint latent normal model for ordinal data, which is an approach that is much more capable to reflect how different questions tend to be correlated. If there are multiple assessments for the same person filling in the questionnaire, one can then even try to capture within person correlations. This kind of approach then has the ability to come up with a more sensible answer to our example above.
