Designing a K-Nearest Neighbour (k-NN) Classifier for Exam Pass/Fail Prediction

1. Choose the attributes (features)

From the given table, use prediction-relevant attributes and drop identifiers:

Attribute	Type	Role
ID, Cell No.	identifier	ignored (no predictive value)
Language	categorical (nominal): Java/C++/Python	matching feature
Passed all Assignments	binary (Yes/No)	matching feature
GPA	numeric (continuous)	main numeric feature
Passed Exam	binary (Yes/No)	class label to predict

2. Encode attributes for distance computation

• GPA — numeric; normalise it (e.g., min–max or z-score) so its scale does not dominate distances.
• Passed all Assignments — encode as 1 (Yes) / 0 (No).
• Language — a categorical matching indicator: 1 if the student's language equals the new student's language, else 0.
• For "Cell No.", a student's phone number should NOT be used (like an ID — it would destroy the algorithm).

3. Define the distance measure

Combine the per-attribute differences, e.g. the weighted Euclidean distance:

$$d(q, t) = \sqrt{w_g\,(gpa_q - gpa_t)^2 + w_a\,(\text{assign}_q - \text{assign}_t)^2 + w_l\,(\text{lang}_q - \text{lang}_t)^2}$$

with default weights 1 for each feature (GPA already normalised). Binary/categorical features contribute 0 (match) or 1 (mismatch).

4. Choose $k$ and the voting rule

• Use small odd $k$ (typically $k=3$ or $k=5$) to avoid ties.
• Tune $k$ by leave-one-out cross-validation on the 8 training tuples (training set is small — each tuple is the test set once, rest train).
• Voting: assign the new student the majority class ("Passed Exam? = Yes/No") among the $k$ nearest neighbours. Ties broken by nearer neighbours or by choosing the smaller distance sum.

5. Evaluation

Compute the classifier's accuracy = (correct predictions)/(total test tuples), and measure the confusion matrix showing false positives (predicted pass, actually failed) vs false negatives — important because failing a student who would pass is arguably worse.

6. Algorithm summary

1. Store all training tuples (X, y): X = (GPA, Assign, Language), y = PassedExam.
2. For a new student q:
      a. normalise GPA features consistently;
      b. compute d(q, t_i) for every stored tuple;
      c. take the k tuples with smallest distance;
      d. output = majority class among those k neighbours.
3. Tune k (and weights) by leave-one-out cross-validation.

This design uses the given table as the training set and predicts Passed Exam for any new student using their GPA, assignment performance, and programming language similarity.