Biostatistics: coefficient of variation: practice question

A PSM question in the style of the NEET PG paper. Answer it first, then read why the right option is right and why each of the others is wrong.

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PSM · Biostatistics: coefficient of variation

Sample item

In a group of adolescents the mean height is 160 cm with an SD of 8 cm, and the mean weight is 50 kg with an SD of 7.5 kg. Which variable shows greater relative variability?

AWeight, because its coefficient of variation is 15% against 5% for heightBHeight, because its mean is largerCBoth equally, because the two SDs are similarDHeight, because its SD of 8 is larger than 7.5

Original practice item, not a recalled exam question. Nothing here is recorded.

The answer and the reasoning

A. Weight, because its coefficient of variation is 15% against 5% for height

The coefficient of variation is SD divided by mean times 100, which makes it unit-free and suitable for comparing variables measured in different units. For height it is 8/160 = 5%, and for weight it is 7.5/50 = 15%. Weight is therefore three times as variable relative to its mean.

Option by option

A. Weight, because its coefficient of variation is 15% against 5% for height (correct)
Correct. CV of weight is 15% and CV of height is 5%.
B. Height, because its mean is larger
A larger mean does not mean more variability; relative variability depends on the SD in proportion to the mean.
C. Both equally, because the two SDs are similar
Similar SD values in different units say nothing about relative spread; the CVs are 15% and 5%.
D. Height, because its SD of 8 is larger than 7.5
The raw SDs are in different units (cm and kg) and cannot be compared directly.

Source note: Original NextPrep sample item — pending expert review. This item is original practice material awaiting independent expert review, so confirm important facts in a standard textbook.

Questions about this PSM question

What is the answer to this PSM question?

The best answer is A, Weight, because its coefficient of variation is 15% against 5% for height. The coefficient of variation is SD divided by mean times 100, which makes it unit-free and suitable for comparing variables measured in different units.

Why is "Height, because its mean is larger" not the answer?

A larger mean does not mean more variability; relative variability depends on the SD in proportion to the mean.

Why is "Both equally, because the two SDs are similar" not the answer?

Similar SD values in different units say nothing about relative spread; the CVs are 15% and 5%.

Why is "Height, because its SD of 8 is larger than 7.5" not the answer?

The raw SDs are in different units (cm and kg) and cannot be compared directly.

What concept does this question test?

It tests Biostatistics: coefficient of variation in PSM. For height it is 8/160 = 5%, and for weight it is 7.5/50 = 15%. Weight is therefore three times as variable relative to its mean.

How hard is this question?

We tag it as a multi-step question: it asks you to combine more than one idea. The tag is our own editorial judgement, not an official difficulty rating, so read the reason for every option, not only the answer.

How should I study Biostatistics: coefficient of variation?

Practise biostatistics with small calculations until sensitivity, predictive values and risk measures are automatic. Then use the flashcards and the other PSM questions on this site to test what stuck.

Is this a real NEET PG question?

No. It is an original practice item (editorial status: sample, version 1). NextPrep does not publish recalled or leaked questions, and independent faculty review of this item has not been completed yet, so confirm important facts in a standard textbook.