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Discrimination index D is the difference in success rate between the top and bottom performing groups, usually the upper and lower 27%. With 24 of 30 correct in the top group and 9 of 30 in the bottom, D is 0.50 - excellent. A negative D means stronger candidates did worse, which almost always signals a mis-keyed or ambiguous item.
Discrimination index
D = (upper correct - lower correct) / group size
Group definition
conventionally the top and bottom 27% of candidates by total score
Kelley showed it maximises the reliability of the difference for a normally distributed trait, balancing group extremity against group size.
Usually a wrong answer key, a misleading distractor or an ambiguous stem. Such items should be removed before scoring.