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Data Mining Exercise 7

For this problem, it is doing Min-Max Normalization. Let's see the answer with a detailed step-by-step method.

Answer

✅ Solution

The new value is 3

$v' = \frac{v - \min_{old}}{\max_{old} - \min_{old}} \times (\max_{new} - \min_{new}) + \min_{new}$

$v (\text{Old value}) = 600$

$\min_{old} (\text{Old min}) = 200$

$\max_{old} (\text{Old max}) = 1,000$

$\min_{new} (\text{New min}) = 1$

$\max_{new} (\text{New max}) = 5$

$v' = \frac{600 - 200}{1000 - 200} \times (5 - 1) + 1$

First part (Find the proportion position):

$\frac{400}{800} = 0.5$

💡 Meaning

Means 600 is exactly in the middle between 200 and 1000.

Second part (Scale to the new range):

$0.5 \times 4 = 2$

Third part (Add the new starting value):

$2 + 1 = \mathbf{3}$

If you don't want to memorize the formula, try imagining a number line:

📊 Visual thinking

Old range: 200 to 1,000 (Distance 800)

New range: 1 to 5 (Distance 4)

✅ Answer

The answer is definitely 3.