In a large dataset of adult heights that follows a perfectly symmetrical distribution, the relationship between the arithmetic mean, median and mode is:

• A Mean is greater than median, which is greater than mode
• B Mean is less than median, which is less than mode
• C Mode is always equal to twice the median minus the mean
• D Mean, median and mode all coincide ✓

Explanation

In a perfectly symmetrical distribution such as the normal curve, the three measures of central tendency are identical because the data balance equally on either side of the centre. Option A describes positive skew and option B describes negative skew. The empirical relation mode equals 3 median minus 2 mean applies only to moderately skewed distributions, so option C does not hold here.

Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.

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