GATE DS&AI 2024 | Question: 17

Question

​​​​​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?

• A. $0.217$
• B. $0.476$
• C. $0.623$
• D. $2.304$

Answer 1

To compute the z-score normalized value, we use the formula:

\[ z = \frac{x - \mu}{\sigma} \]

where:

- \( x \) is the given value (₹106000 in this case),

- \( \mu \) is the mean (₹96000),

- \( \sigma \) is the standard deviation (₹21000).

Substituting the values:

\[ z = \frac{106000 - 96000}{21000} = \frac{10000}{21000} = 0.476 \]

So, the z-score normalized income value of ₹106000 is closest to:
B. 0.476