What does StandardScaler do?

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 Perfect, let’s carefully analyze this code step by step.

Code Recap

import pandas as pd
from sklearn.preprocessing import StandardScaler

data = pd.DataFrame({
    'col1': [1, 2, 3, 4, 5],
    'col2': [10, 20, 30, 40, 50]
})

ss = StandardScaler()
scaled_data = ss.fit_transform(data)
print(ss.var_)

We are asked: What will ss.var_ print?

Step 1: What does StandardScaler do?

  • It standardizes features by removing the mean and scaling to unit variance.

  • Internally, it computes:

    var_=∑(xi−μ)2n\text{var\_} = \frac{\sum (x_i - \mu)^2}{n}

    👉 Notice: StandardScaler uses population variance (divide by n), not sample variance (which divides by n-1).

Step 2: Compute variance for col1

col1 = [1, 2, 3, 4, 5]

  • Mean = (1+2+3+4+5)/5=15/5=3(1+2+3+4+5)/5 = 15/5 = 3

var=(1−3)2+(2−3)2+(3−3)2+(4−3)2+(5−3)25\text{var} = \frac{(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2}{5} =4+1+0+1+45=105=2= \frac{4 + 1 + 0 + 1 + 4}{5} = \frac{10}{5} = 2

So, var(col1) = 2.

Step 3: Compute variance for col2

col2 = [10, 20, 30, 40, 50]

  • Mean = (10+20+30+40+50)/5=150/5=30(10+20+30+40+50)/5 = 150/5 = 30

var=(10−30)2+(20−30)2+(30−30)2+(40−30)2+(50−30)25\text{var} = \frac{(10-30)^2 + (20-30)^2 + (30-30)^2 + (40-30)^2 + (50-30)^2}{5} =400+100+0+100+4005=10005=200= \frac{400 + 100 + 0 + 100 + 400}{5} = \frac{1000}{5} = 200

So, var(col2) = 200.

Step 4: Final Answer

ss.var_ = [2, 200]

✅ Correct Option: [2, 200]

Would you like me to also explain why the other options are wrong (e.g., why [4,400] or [10,10000] appear as distractors)?

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