GATE 2024 DA Q.27: solution and answer

GATE 2024 · DAQ.27 · 1 mark · MCQ

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

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Answer and solution

ANSWER

The z-score is 10/21, about 0.476, so the answer is option (B).

Official answer: BSource: Official answer key, GATE 2024 DA (IISc Bengaluru)

Z-score normalization rescales a value using the attribute's mean and standard deviation: $z = \frac{x - μ}{σ}$ .
The minimum (46000) and maximum (170000) are not needed. They belong to min-max normalization, so here they are distractors.
Substitute $x = 106000$ , $μ = 96000$ , $σ = 21000$ : $z = \frac{106000 - 96000}{21000} = \frac{10000}{21000} = \frac{10}{21} .$
Compute: $\frac{10}{21} \approx 0.47619$ , which is closest to $0.476$ , option (B).
Check against the distractor: min-max normalization would give $\frac{106000 - 46000}{170000 - 46000} = \frac{60000}{124000} \approx 0.484$ . That is a different quantity and matches no option exactly, so the z-score value $0.476$ is the answer. The other options do not fit: $0.217$ , $0.623$ and $2.304$ are far from $\frac{10}{21}$ .

KEY IDEA

Z-score normalization uses only the mean and standard deviation: z = (x − mean) / standard deviation. Minimum and maximum are used by min-max normalization, not here.

WATCH OUT FOR

Using the minimum and maximum (min-max scaling) gives about 0.484, which is near 0.476 and can tempt you to pick the wrong method. Check that the question asks for the z-score.

From the GATE 2024 DA paper. Every question of this paper · Download the full paper · All 1 Data transformation questions, with notes