### Point of Maximum Information

To grasp the concept of Point of Maximum Information (PMI), it is helpful to first understand the term item discrimination
The Point of Maximum Information (PMI) in Item Response Theory (IRT) refers to the IQ level at which a question has the highest item discrimination. This means that the difference in probability of a correct response between test-takers at the Point of Maximum Information level and those with higher or lower IQ levels is the greatest.
A simple example: If you ask a group of math students the question, "What is 5 x 10 + 10?", all of the students will know the answer. However, if you ask the same question to a group of 6-year-olds, only a few will likely know the answer, and if you ask it to a group of 3-year-olds, no one will know the answer. The question is more effective at distinguishing among the abilities of 6-year-olds than it is among math students or 3-year-olds. You could say that the item discrimination of this question is the highest around the age of 6, so the point of maximum information of this question is also around that age. The same principle applies to IQ test questions, but in this case, the point of maximum information is expressed in IQ level.
The Point of Maximum Information can be seen in the Item Characteristic Curve.
The Point of Maximum Information for the question that belongs to this ICC is around 117. If you were to ask this question to someone with an IQ below 100 or above 130, the answer would provide (almost) no information about the test taker. Individuals with an IQ below 100 probably guessed the correct answer if they provided it. On the other hand, individuals with an IQ above 130 would likely always give the correct answer, making the question redundant for them.
Based on the ICC, it is possible to create a graph about the amount of information that the question gives about the test taker with a given IQ. The Item Information Curve is based on the slope (the derivative) of the Item Characteristic Curve.
The Item Information Curve of the question that belongs to the ICC above, would look something like this.