GATE 2023 ST – Question 7

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

For the probability mass function P(x) shown, which relation between mean,median and mode follows?

mean = median ≠ mode
mean = median = mode
mean ≠ median = mode
mean ≠ mode = median

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Show answer and explanation

Correct answer: (A) mean = median ≠ mode

Explanation

The plotted masses are symmetric about zero, so the mean is zero and zero is a median. The tallest masses occur at the two symmetric off-center peaks, not at zero. Thus mean and the central median agree and differ from the modes. **A**. For discrete distributions a median may be nonunique; the comparison uses the central median indicated by symmetry.

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