Birth weight in hospital A has a mean of 3.0 kg with a standard deviation of 0.45 kg. Head circumference in the same nursery has a mean of 34 cm with a standard deviation of 1.7 cm. To decide which of the two measurements shows greater relative variability, the appropriate statistic is:

• A Standard deviation alone
• B Variance
• C Range
• D Coefficient of variation ✓

Explanation

The coefficient of variation expresses the standard deviation as a percentage of the mean, allowing comparison of variability between distributions measured in different units. Here birth weight gives a CV of 15% and head circumference a CV of 5%, showing birth weight is relatively more variable despite the much larger absolute standard deviation of head circumference in centimetres being misleading. Standard deviation and variance carry units and cannot be compared across different measurements.

Reference: Mahajan's Methods in Biostatistics for Medical Students and Research Workers, 10th ed.

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Written and medically reviewed by the StethoPrep medical team.