Question $5$:

$5\mathrm{.}1$ An IR system returns $8$ relevant documents, and $10$ nonrelevant documents. There are a total of $20$ relevant documents in the collection. What is the precision of the system on this search, and what is its recall?

$5\mathrm{.}2$ The following list of $R$ s and $N$ s represents relevant $(R)$ and nonrelevant $(N)$ returned documents in a ranked list of $20$ documents retrieved in response to a query from a collection of $10,000$ documents. The top of the ranked list $($the document the system thinks is most likely to be relevant$)$ is on the len of the list. This list shows $6$ relevant documents. Assume that there are $8$ relevant documents in total in the collection.

R RNNNNNN RNRNNNRNNNN R

a$.$ What is the precision of the system on the top $20?$

b$.$ What is the Fl on the top $20?$

c$.$ What is the unimerpolated precision of the system at $25\%$ recall?

d$.$ What is the interpolated precision at $33\%$ recall?