Q.4 Which one among the following statements must be TRUE about the mean and the
median of the scores of all candidates appearing for GATE 2023?
(A) The median is at least as large as the mean.
(B) The mean is at least as large as the median.
(C) At most half the candidates have a score that is larger than the median.
(D) At most half the candidates have a score that is larger than the mean.
GATE 2023 Mean vs Median: Correct Answer Revealed
The correct statement that must always be true about the mean and median of GATE 2023 candidate scores is option (C): At most half the candidates have a score larger than the median. This holds due to the median’s definition as the central value in any dataset. Options (A), (B), and (D) depend on score distribution and are not universally true.
Mean and Median Definitions
The mean equals the total scores divided by candidate count, sensitive to extremes like top ranks pulling it higher. The median is the middle score when sorted, splitting data so exactly 50% (or at most half in ties) exceed it.
Option Analysis
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(A) Median ≥ Mean: False in right-skewed distributions like exam scores, where few high scores raise the mean above the median.
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(B) Mean ≥ Median: Not always true; left-skewed data (many high, few low scores) makes median larger.
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(C) ≤ Half above median: Always true by definition—median ensures half or fewer scores exceed it.
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(D) ≤ Half above mean: False; skewness allows over half below mean if outliers dominate.
Why (C) for GATE Scores
GATE distributions are typically right-skewed, but median property remains universal regardless of shape or GATE 2023 specifics.
GATE 2023 aspirants often face tricky stats questions on GATE 2023 mean median relationships in competitive exams like GATE and CSIR NET. This GATE 2023 mean and median query tests core statistical properties applicable to candidate scores.
Core Concepts
Mean averages all scores but shifts with outliers. Median resists this, always dividing data evenly.
Breaking Down Options
| Option | Statement | True? | Reason |
|---|---|---|---|
| A | Median ≥ mean | No | Fails in right-skew (common in exams) |
| B | Mean ≥ median | No | Fails in left-skew |
| C | ≤ Half > median | Yes | Definitional—50th percentile |
| D | ≤ Half > mean | No | Skewness allows >half below mean |
GATE 2023 Relevance
Exam scores skew right, but only median’s half-above property is must be true universally.
Master GATE 2023 mean median for quant sections—practice skewed distributions next!
