Question 1

Which of the following best describes the concept of a 'sample' in statistics?

Accepted Answer

A sample is a subset of observations selected from a population to represent it.

Question 2

Given a population with values $$X_1$$, $$X_2$$, \ldots, X_N$$, which formula correctly represents the population mean?

Accepted Answer

$$\mu = \dfrac{\sum_{i=1}^{N} X_i}{N}$$

Question 3

A researcher wants to estimate the average height of university students. She measures the heights of 50 randomly selected students. What is the term for the average height calculated from these 50 students?

Accepted Answer

Sample mean

Question 4

Which equation correctly represents the sample mean for a sample of size $$n$$ with observations $$X_1$$, $$X_2$$, \ldots, X_n$$?

Accepted Answer

$$\bar{X} = \dfrac{\sum_{i=1}^{n} X_i}{n}$$

Question 5

Suppose you have a population of exam scores: 70, 80, 90, 100. What is the population mean?

Accepted Answer

$$\mu = 85$$

Question 6

Why is it important to use a sample rather than the entire population in many statistical studies?

Accepted Answer

Because it is often impractical or impossible to collect data from the entire population.

Question 7

If a sample consists of the following values: 5, 7, 9, what is the sample mean?

Accepted Answer

$$\bar{X} = 7$$

Question 8

A population consists of $$N = 5$$ values: $$2, 4, 6, 8, 10. $$Calculate the population mean using the correct formula.

Accepted Answer

$$\mu = 6$$

Question 9

Which of the following statements is TRUE regarding the relationship between a sample and a population?

Accepted Answer

A sample is a subset of the population used to make inferences about the population.

Question 10

A medical researcher collects blood pressure readings from 100 patients to estimate the average blood pressure in the city. What statistical concept is being applied?

Accepted Answer

Using a sample to estimate a population parameter

Question 11

If the sample mean is calculated as $$\bar{X} = 12$$ from a sample of $$n = 4$$ observations, what is the sum of the sample values?

Accepted Answer

$$\sum_{i=1}^{4} X_i = 48$$

Question 12

Which of the following is NOT a reason for using samples in statistical analysis?

Accepted Answer

Samples always provide the exact population parameter.

Question 13

A population consists of $$N = 3$$ values: $$4, 8, 12. $$What is the population mean?

Accepted Answer

$$\mu = 8$$

Question 14

Which formula would you use to calculate the mean of a sample with $$n$$ observations?

Accepted Answer

$$\bar{X} = \dfrac{\sum_{i=1}^{n} X_i}{n}$$

Question 15

A sample of $$n = 5$$ students has test scores: 60, 70, 80, 90, 100. What is the sample mean?

Accepted Answer

$$\bar{X} = 80$$

Question 16

In a study, the population mean is known to be $$\mu = 50. A $$sample of $$n = 4 is $$taken with values 45, 55, 50, 60. What is the sample mean?

Accepted Answer

$$\bar{X} = 52.5$$

Question 17

Which of the following best explains the difference between a sample mean and a population mean?

Accepted Answer

The sample mean is calculated from a subset of the population, while the population mean uses all members.

Question 18

A population consists of $$N = 6$$ values: $$3, 6, 9, 12, 15, 18. $$What is the population mean?

Accepted Answer

$$\mu = 10.5$$

Question 19

If a sample of $$n = 3$$ has values $$2, 4, 6$$, what is the sample mean?

Accepted Answer

$$\bar{X} = 4$$

Question 20

A population has $$N = 4$$ values: $$5, 10, 15, 20. $$What is the population mean?

Accepted Answer

$$\mu = 12.5$$

Fundamental Concepts in Statistics: Population, Sample, and Sample Mean

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