Apply Weighted KNN Algorithm using the given dataset to classify the test set data (7.6, 60, 8) where k = 3

Apply Weighted KNN Algorithm using the given dataset to classify the test set data (7.6, 60, 8) where k = 3

Answer:-

Let’s apply the Weighted K-Nearest Neighbors (KNN) algorithm step-by-step to classify the test data point (CGPA = 7.6, Assessment = 60, Project Submitted = 8) using the given dataset and k=3k = 3.

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Step 1: Training Data

S.No	CGPA	Assessment	Project	Result
1	9.2	85	8	Pass
2	8.0	80	7	Pass
3	8.5	81	8	Pass
4	6.0	45	5	Fail
5	6.5	50	4	Fail
6	8.2	72	7	Pass
7	5.8	38	5	Fail
8	8.9	91	9	Pass

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Step 2: Test Point

Test instance:
(x1,x2,x3)=(7.6, 60, 8)(x_1, x_2, x_3) = (7.6,\ 60,\ 8)

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Step 3: Distance Calculation (Euclidean Distance)

Distance formula: d=(x1−xi)2+(x2−yi)2+(x3−zi)2d = \sqrt{(x_1 – x_i)^2 + (x_2 – y_i)^2 + (x_3 – z_i)^2}

We’ll compute distance from test point to each record:

S.No	CGPA	Assess	Project	Result	Distance
1	9.2	85	8	Pass	√((7.6−9.2)² + (60−85)² + (8−8)²) = √((−1.6)² + (−25)²) = √(2.56 + 625) = √627.56 ≈ 25.05
2	8.0	80	7	Pass	√((−0.4)² + (−20)² + 1²) = √(0.16 + 400 + 1) = √401.16 ≈ 20.02
3	8.5	81	8	Pass	√((−0.9)² + (−21)²) = √(0.81 + 441) = √441.81 ≈ 21.02
4	6.0	45	5	Fail	√((1.6)² + (15)² + 3²) = √(2.56 + 225 + 9) = √236.56 ≈ 15.38
5	6.5	50	4	Fail	√((1.1)² + 10² + 4²) = √(1.21 + 100 + 16) = √117.21 ≈ 10.82
6	8.2	72	7	Pass	√((−0.6)² + (−12)² + 1²) = √(0.36 + 144 + 1) = √145.36 ≈ 12.05
7	5.8	38	5	Fail	√((1.8)² + 22² + 3²) = √(3.24 + 484 + 9) = √496.24 ≈ 22.28
8	8.9	91	9	Pass	√((−1.3)² + (−31)² + (−1)²) = √(1.69 + 961 + 1) = √963.69 ≈ 31.03

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Step 4: Select K = 3 Nearest Neighbors

Sort by distance:

S.No	Result	Distance
5	Fail	10.82
6	Pass	12.05
4	Fail	15.38

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Step 5: Compute Weighted Vote

We assign weight w=1dw = \frac{1}{d}

S.No	Result	Distance	Weight (1/d)
5	Fail	10.82	0.0924
6	Pass	12.05	0.0830
4	Fail	15.38	0.0650

Total Weights:

• Fail = 0.0924 + 0.0650 = 0.1574
• Pass = 0.0830

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Step 6: Final Prediction

Since Fail has a higher total weight than Pass:

Predicted Result = Fail