Question: In binary classification, explain how the F1 score is constructed, why it is often favored over a plain average of precision and recall, and what the main objections to using it are.

Sample answer: The F1 score combines precision and recall with the harmonic mean, so it is computed as 2PR/(P+R), where P is precision and R is recall. This form is usually preferred to the ordinary arithmetic mean because it penalizes imbalance: a model cannot score well if one of the two quantities is very low, even if the other is high. The metric is criticized for two main reasons. It forces precision and recall to matter equally, even when a task would value one more than the other. It also leaves out true negatives, which can make it a poor summary measure when one class is much more common than the other.

Key points:

• F1 score uses the harmonic mean of precision and recall.
• Its formula is 2PR/(P+R).
• The harmonic mean downweights cases where precision and recall are far apart.
• It assigns the same weight to precision and recall.
• It does not use true negatives, so it can be misleading on heavily imbalanced data.

Rubric: A full-credit response must state that F1 is the harmonic mean of precision and recall, give the formula, explain why that mean is preferred over a simple average, and identify both major criticisms: equal weighting of precision and recall and omission of true negatives.