Listing all possible samples of size two

Oct 13, 2025 by leolavanderia.com.br 0 views

Introduction

In statistics, a sample is a subset of a population that is used to make inferences about the population as a whole. When we take a sample from a population, we can calculate various statistics such as the sample mean, sample range, and sample maximum. In this article, we will list all possible samples of size two from the population {10, 20, 30, 40} and compute the sample mean, sample range, and sample maximum for each sample.

Listing all possible samples of size two

To list all possible samples of size two from the population {10, 20, 30, 40}, we need to choose two numbers from the population. We can do this in the following ways:

Choose the first number from the population and then choose the second number from the remaining numbers in the population.
Choose the first number from the population and then choose the second number from the entire population.

Using this approach, we can list all possible samples of size two from the population {10, 20, 30, 40} as follows:

Sample	1st Number	2nd Number
1	10	20
2	10	30
3	10	40
4	20	30
5	20	40
6	30	40

Computing the sample mean

The sample mean is the average of the two numbers in the sample. We can compute the sample mean for each sample as follows:

For sample 1, the sample mean is (10 + 20) / 2 = 15.
For sample 2, the sample mean is (10 + 30) / 2 = 20.
For sample 3, the sample mean is (10 + 40) / 2 = 25.
For sample 4, the sample mean is (20 + 30) / 2 = 25.
For sample 5, the sample mean is (20 + 40) / 2 = 30.
For sample 6, the sample mean is (30 + 40) / 2 = 35.

Computing the sample range

The sample range is the difference between the largest and smallest numbers in the sample. We can compute the sample range for each sample as follows:

For sample 1, the sample range is 20 - 10 = 10.
For sample 2, the sample range is 30 - 10 = 20.
For sample 3, the sample range is 40 - 10 = 30.
For sample 4, the sample range is 30 - 20 = 10.
For sample 5, the sample range is 40 - 20 = 20.
For sample 6, the sample range is 40 - 30 = 10.

Computing the sample maximum

The sample maximum is the largest number in the sample. We can compute the sample maximum for each sample as follows:

For sample 1, the sample maximum is 20.
For sample 2, the sample maximum is 30.
For sample 3, the sample maximum is 40.
For sample 4, the sample maximum is 30.
For sample 5, the sample maximum is 40.
For sample 6, the sample maximum is 40.

Summary

In this article, we listed all possible samples of size two from the population {10, 20, 30, 40} and computed the sample mean, sample range, and sample maximum for each sample. We found that the sample mean, sample range, and sample maximum vary depending on the sample chosen. This highlights the importance of taking multiple samples from a population to make accurate inferences about the population.

Conclusion

In conclusion, listing all possible samples of size two from a population and computing the sample mean, sample range, and sample maximum can provide valuable insights into the population. By understanding the properties of the sample, we can make more accurate inferences about the population and make better decisions.

Introduction

In our previous article, we listed all possible samples of size two from the population {10, 20, 30, 40} and computed the sample mean, sample range, and sample maximum for each sample. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q&A

Q1: What is the difference between a population and a sample?

A1: A population is the entire set of data that we are interested in, while a sample is a subset of the population that is used to make inferences about the population.

Q2: How do we choose a sample from a population?

A2: We can choose a sample from a population using various methods such as random sampling, stratified sampling, and systematic sampling.

Q3: What is the sample mean?

A3: The sample mean is the average of the numbers in the sample. It is calculated by summing up all the numbers in the sample and dividing by the number of observations.

Q4: What is the sample range?

A4: The sample range is the difference between the largest and smallest numbers in the sample.

Q5: What is the sample maximum?

A5: The sample maximum is the largest number in the sample.

Q6: How do we compute the sample mean, sample range, and sample maximum?

A6: We can compute the sample mean, sample range, and sample maximum by following the formulas:

Sample mean = (sum of all numbers in the sample) / (number of observations)
Sample range = largest number - smallest number
Sample maximum = largest number in the sample

Q7: Why is it important to take multiple samples from a population?

A7: Taking multiple samples from a population helps to reduce the effect of sampling error and provides a more accurate estimate of the population parameters.

Q8: What are some common types of sampling methods?

A8: Some common types of sampling methods include:

Random sampling
Stratified sampling
Systematic sampling
Cluster sampling
Convenience sampling

Q9: What are some common applications of sampling in statistics?

A9: Some common applications of sampling in statistics include:

Estimating population parameters
Making inferences about a population
Testing hypotheses about a population
Predicting future outcomes

Q10: What are some common challenges associated with sampling?

A10: Some common challenges associated with sampling include:

Sampling bias
Non-response bias
Sampling error
Limited sample size

Conclusion

In conclusion, sampling is an important concept in statistics that helps us to make inferences about a population. By understanding the different types of sampling methods and the formulas for computing sample statistics, we can make more accurate estimates of population parameters and make better decisions.

Frequently Asked Questions

Q11: What is the difference between a sample and a population?

A11: A sample is a subset of the population that is used to make inferences about the population, while a population is the entire set of data that we are interested in.

Q12: How do we choose a sample from a population?

A12: We can choose a sample from a population using various methods such as random sampling, stratified sampling, and systematic sampling.

Q13: What is the sample mean?

A13: The sample mean is the average of the numbers in the sample. It is calculated by summing up all the numbers in the sample and dividing by the number of observations.

Q14: What is the sample range?

A14: The sample range is the difference between the largest and smallest numbers in the sample.

Q15: What is the sample maximum?

A15: The sample maximum is the largest number in the sample.

Additional Resources

For more information on sampling and statistics, please refer to the following resources:

[1] Wikipedia: Sampling (statistics)
[2] Khan Academy: Sampling and statistics
[3] Stat Trek: Sampling and statistics
[4] Math Is Fun: Sampling and statistics

Note: The above resources are for educational purposes only and are not affiliated with any particular organization or company.