If we are looking at the average IQ of all Americans by examining a sample of 50 people, which of the following is true?

I. The average IQ of the sample could be greater than the average IQ of the population.
II. The average IQ of the sample could be smaller than the average IQ of the population.
III. The average IQ of the sample must be the same as the average IQ of the population.

a. I and II
b. I only
c. II only
d. III

Question

31-08-2025
Social Studies

High School

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If we are looking at the average IQ of all Americans by examining a sample of 50 people, which of the following is true?

I. The average IQ of the sample could be greater than the average IQ of the population.
II. The average IQ of the sample could be smaller than the average IQ of the population.
III. The average IQ of the sample must be the same as the average IQ of the population.

a. I and II
b. I only
c. II only
d. III

Answer :

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annaiselvam annaiselvam · Answer 1 · 2024-07-11T11:15:56-04:00

Final answer:

The average IQ of a sample of 50 people could either be higher or lower than the population average due to sampling variability. The sample average does not necessarily have to be the same as the population average. Therefore option a. I and II

Explanation:

When looking at the average IQ of all Americans by looking at a sample of 50 people, it is important to understand the concept of sampling variability. The following statements can be assessed:

The average IQ of the sample could be greater than the average IQ of the population.
The average IQ of the sample could be smaller than the average IQ of the population.
The average IQ of the sample must be the same as the average IQ of the population.

The correct answer is that both I and II are true. It is entirely possible for the average IQ of a sample of 50 people to be either higher or lower than the population average due to natural fluctuations in sample selection. Therefore, the average IQ of the sample does not have to be the same as the population average, making statement III incorrect. Thus, the correct option is a. I and II.