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GATE 2023 CE (CE2) – Question 12

Engineering Mathematics · Probability and Statistics: Probability, conditional probability, descriptive statistics · 1 mark · Multiple choice

Which of the following probability distribution functions (PDFs) has the mean greater than the median?

Function 1 is symmetric unimodal, Function 2 has a long right tail, Function 3 has a long left tail, Function 4 is symmetric bimodal.
  1. Function 1
  2. Function 2
  3. Function 3
  4. Function 4

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Show answer and explanation

Correct answer: (B) Function 2

Explanation

**Mean versus median and skewness.**
- For a **symmetric** distribution (Functions 1 and 4), the mean equals the median.
- For a **right-skewed** distribution (a long tail to the right), the few very large values pull the mean up past the median, so mean > median.
- For a **left-skewed** distribution (a long tail to the left), the mean is pulled below the median.

Function 2 has the long right tail, so its mean is greater than its median. Function 3 (left tail) has mean < median.

Answer **Function 2** (B).