Biostatistics: effect of linear transformation: 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: effect of linear transformation

Sample item

Body temperatures in a sample have a mean of 37.0 degrees Celsius and a standard deviation of 0.5. The values are converted to Fahrenheit using F = 1.8C + 32. What are the new mean and standard deviation?

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

The answer and the reasoning

C. Mean 98.6, standard deviation 0.9

Multiplying every value by a constant multiplies the mean and the standard deviation by that constant. Adding a constant shifts the mean but leaves the standard deviation unchanged. The mean is 1.8 x 37 + 32 = 98.6 and the standard deviation is 1.8 x 0.5 = 0.9.

Option by option

  • A. Mean 98.6, standard deviation 0.5

    The SD changes with the multiplier of 1.8, so it cannot remain 0.5.

  • B. Mean 98.6, standard deviation 32.9

    The added 32 shifts values but does not enter the standard deviation.

  • C. Mean 98.6, standard deviation 0.9 (correct)

    Correct. The mean is scaled and shifted while the SD is only scaled.

  • D. Mean 66.6, standard deviation 0.9

    This forgets to add 32 to the mean; the SD is correct.

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.

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Questions about this PSM question

What is the answer to this PSM question?

The best answer is C, Mean 98.6, standard deviation 0.9. Multiplying every value by a constant multiplies the mean and the standard deviation by that constant.

Why is "Mean 98.6, standard deviation 0.5" not the answer?

The SD changes with the multiplier of 1.8, so it cannot remain 0.5.

Why is "Mean 98.6, standard deviation 32.9" not the answer?

The added 32 shifts values but does not enter the standard deviation.

Why is "Mean 66.6, standard deviation 0.9" not the answer?

This forgets to add 32 to the mean; the SD is correct.

What concept does this question test?

It tests Biostatistics: effect of linear transformation in PSM. Adding a constant shifts the mean but leaves the standard deviation unchanged. The mean is 1.8 x 37 + 32 = 98.6 and the standard deviation is 1.8 x 0.5 = 0.9.

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: effect of linear transformation?

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.