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.

For which reason can't you use fractions in imputation? Based on that you will have to decide on an alternative.
For instance, it might be that the variable is categorical and you can't use numbers in the regression model. In that case, you could impute the categories (you could impute each category once with a weight depending on the frequency that the category occurs).
