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The procedure for replacing missing data by the average of a particular category typically involves the following steps:

1. Identify the category to which the missing data belongs.
2. Calculate the average (or mean) of the available data within that category.
3. Replace the missing data with the calculated average.

For example, let's say we have a dataset that includes age and income information for a group of people, but some of the income values are missing. We want to fill in these missing values by the average income of people within the same age group. We would follow these steps:

1. Identify the age group to which the missing data belongs.
2. Calculate the average income for people within that age group.
3. Replace the missing income value with the calculated average.

Note that this procedure assumes that the missing data is missing at random (MAR), and that the available data within each category is representative of the entire category.