Applying k-NN — Predict Student 9's Re-exam Result

Student 9 to classify

ID	Language	Passed all Assignments	GPA	Passed Exam
9	C++	Yes	3.0	??

The training set is table Q5a; I use the features (GPA, Passed all Assignments, Language = C++) with the distance

$$d = \sqrt{(\Delta\text{GPA})^2 + (\Delta\text{Assign})^2 + (\Delta\text{Language})^2}$$

where mismatches count 1. (Normalisation is omitted here only for a clean illustration; in real use GPA would first be min–max normalised.)

Distances from student 9 to every training tuple

T	Language	Assign	GPA	Passed Exam	ΔGPA	ΔAssign	ΔLang	d
1	Java	No	3.1	Yes	0.1	1	1	1.42
2	Java	No	2.0	No	1.0	1	1	1.73
3	C++	Yes	3.5	Yes	0.5	0	0	0.50
4	Python	Yes	2.5	Yes	0.5	0	1	1.12
5	Java	Yes	3.9	No	0.9	0	1	1.35
6	C++	No	2.9	No	0.1	1	0	1.00
7	Java	No	1.9	No	1.1	1	1	1.79
8	Python	Yes	3.2	Yes	0.2	0	1	1.02

k = 3 nearest neighbours

Closest three tuples: #3 (d=0.50, Pass=Yes), #6 (d=1.00, Pass=No), #8 (d=1.02, Pass=Yes).

• Voting: Yes (2) vs No (1) → majority class = Yes.

Answer

Student 9 (C++, passed all assignments, GPA 3.0) is predicted to PASS the re-exam under a k=3 nearest-neighbour classifier.

(Note: if GPA were normalised the ranking could shift slightly, but the closest student #3 — identical language, same assignment status, close GPA — strongly dominates the vote; the same conclusion typically holds for k=1, 3 and 5.)