Biostatistics: central limit theorem: 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: central limit theorem

Sample item

Birth weights in a hospital are skewed. A researcher draws many random samples of 100 babies and calculates the mean of each sample. What is expected of the distribution of these sample means?

AIt has a larger spread than the birth weights themselvesBIt is approximately normal even though the birth weights are skewedCIt is uniform across the range of birth weightsDIt is skewed in the same way as the birth weights

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

The answer and the reasoning

B. It is approximately normal even though the birth weights are skewed

By the central limit theorem, the distribution of sample means approaches normal as the sample size grows, whatever the shape of the underlying distribution. Its spread is the standard error, which is smaller than the standard deviation of individual values. This underpins confidence intervals and many significance tests.

Option by option

A. It has a larger spread than the birth weights themselves
The spread of sample means, the standard error, is smaller than that of individual values.
B. It is approximately normal even though the birth weights are skewed (correct)
Correct. Means of reasonably large samples are approximately normal despite skewed raw data.
C. It is uniform across the range of birth weights
Sample means cluster around the true mean and do not spread uniformly.
D. It is skewed in the same way as the birth weights
The skewness of raw data does not carry over to the distribution of means of large samples.

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 B, It is approximately normal even though the birth weights are skewed. By the central limit theorem, the distribution of sample means approaches normal as the sample size grows, whatever the shape of the underlying distribution.

Why is "It has a larger spread than the birth weights themselves" not the answer?

The spread of sample means, the standard error, is smaller than that of individual values.

Why is "It is uniform across the range of birth weights" not the answer?

Sample means cluster around the true mean and do not spread uniformly.

Why is "It is skewed in the same way as the birth weights" not the answer?

The skewness of raw data does not carry over to the distribution of means of large samples.

What concept does this question test?

It tests Biostatistics: central limit theorem in PSM. Its spread is the standard error, which is smaller than the standard deviation of individual values. This underpins confidence intervals and many significance tests.

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: central limit theorem?

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.