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GATE 2023 CE (CE1) – Question 7

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), $P(x)$, of a variable $x$?

a histogram of $P(x)$ for $x$ from −17 to 17, symmetric about $x = 0$. It has two tall peaks, at about $x = -13$ and $x = 13$, and a lower local peak at the centre.
  1. mean = median ≠ mode
  2. mean = median = mode
  3. mean ≠ median = mode
  4. mean ≠ mode = median

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Show answer and explanation

Correct answer: (A) mean = median ≠ mode

Explanation

The distribution is symmetric about $x = 0$, so the mean and the median are both at the centre, 0. The highest bars (the modes) are at $x = \pm 13$, where there are two equal peaks, so the mode is not at the centre. So mean = median ≠ mode.