If we consider all the terms with the same importance for all the queries, it will not work for all queries. If the documents are related to ice, it is obvious that "ice" will be in almost all documents, probably with high frequency. Collection frequency and document frequency are two different terms that need to be explained. A collection contains many documents. The collection frequency (cf) shows the frequency of terms (t) in all documents in the collection, whereas the document frequency (df) shows the frequency of t in a single document. So the word "ice" will have a high collection frequency, as it is presumed to appear in all the documents in the collection. A simple idea is to reduce the weight of such terms if they have a high collection frequency. Inverse frequency is defined as follows:
Here, N is the total number of documents in a collection. The idf of a frequent term is likely to be low, and that of a rare term will be high.