GATE DA 2024 | Question 27
Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹46000, ₹170000, ₹96000, and ₹21000, respectively. The z-score normalized income value of ₹106000 is closest to which ONE of the following options?
Explanation
Answer: (B)
z-score normalization subtracts the mean and divides by the standard deviation:
\[z = \frac{x - \mu}{\sigma} = \frac{106000 - 96000}{21000} = \frac{10000}{21000} \approx 0.476.\]
The minimum and maximum play no part here. They are what min-max normalization uses, and that would give \(\frac{106000 - 46000}{170000 - 46000} \approx 0.484\), which is not an option either. Option A divides the difference from the mean by the minimum instead of the standard deviation, and D divides the income itself by the minimum.
Answer: B