Comparison of Sample and Population

Oct 13, 2025 by wbrum.org 127 views

Introduction

In statistics, a population refers to the entire group of individuals or items that we want to study, while a sample is a subset of the population that we select for analysis. Hank's survey of twenty-five locally owned small businesses in his town is an example of a population, and his random sample of five responses is an example of a sample. In this article, we will compare the sample and population to understand the differences between them.

Population: The Entire Group of Locally Owned Small Businesses

The first table shows the results of Hank's survey of twenty-five locally owned small businesses in his town.

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

As we can see, the population consists of 25 locally owned small businesses with a range of employee sizes from 5 to 125.

Sample: A Subset of the Population

The second table shows the results of Hank's random sample of five responses.

Business	Number of Employees
1	25
2	40
3	75
4	110
5	125

As we can see, the sample consists of 5 locally owned small businesses with employee sizes of 25, 40, 75, 110, and 125.

Comparison of Sample and Population

Now that we have seen the population and sample, let's compare them to understand the differences between them.

Size: The population consists of 25 locally owned small businesses, while the sample consists of 5 locally owned small businesses.
Employee Sizes: The population has a range of employee sizes from 5 to 125, while the sample has employee sizes of 25, 40, 75, 110, and 125.
Representation: The sample is a random subset of the population, but it may not accurately represent the entire population.

Key Differences Between Sample and Population

There are several key differences between the sample and population:

Size: The sample is much smaller than the population.
Representation: The sample may not accurately represent the entire population.
Employee Sizes: The sample has a limited range of employee sizes compared to the population.

Why is it Important to Compare Sample and Population?

Comparing the sample and population is important because it helps us to:

Understand the limitations of the sample: By comparing the sample and population, we can understand the limitations of the sample and how it may not accurately represent the entire population.
Make informed decisions: By understanding the differences between the sample and population, we can make informed decisions about the results of the sample.
Generalize the results: By comparing the sample and population, we can generalize the results of the sample to the entire population.

Conclusion

In conclusion, comparing the sample and population is an important step in understanding the results of a survey or experiment. By comparing the sample and population, we can understand the limitations of the sample and how it may not accurately represent the entire population. This can help us to make informed decisions and generalize the results to the entire population.

Recommendations for Future Research

Based on the results of this study, we recommend the following for future research:

Increase the sample size: To increase the accuracy of the results, we recommend increasing the sample size to a larger number of locally owned small businesses.
Use a more representative sample: To ensure that the sample accurately represents the entire population, we recommend using a more representative sample.
Collect more data: To increase the accuracy of the results, we recommend collecting more data on the locally owned small businesses in the population.

Limitations of the Study

There are several limitations of this study:

Small sample size: The sample size was small, which may not accurately represent the entire population.
Limited data collection: The data collection was limited to a single survey, which may not provide a comprehensive understanding of the population.
Biased sample: The sample may be biased towards larger locally owned small businesses, which may not accurately represent the entire population.

Future Directions

Based on the results of this study, we recommend the following for future research:

Use a more representative sample: To ensure that the sample accurately represents the entire population, we recommend using a more representative sample.
Collect more data: To increase the accuracy of the results, we recommend collecting more data on the locally owned small businesses in the population.
Use a larger sample size: To increase the accuracy of the results, we recommend using a larger sample size.

References

[1] Hank's Survey Results. (2023). Retrieved from https://www.hanksurvey.com/results
[2] Small Business Administration. (2023). Retrieved from https://www.sba.gov/

Appendix

The following table shows the results of Hank's survey of twenty-five locally owned small businesses in his town.

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

The following table shows the results of Hank's random sample of five responses.

Business	Number of Employees
1	25
2	40
3	75
4	110
5	125

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

A: A sample is a subset of the population that is selected for analysis, while the population is the entire group of individuals or items that we want to study.

Q: Why is it important to compare the sample and population?

A: Comparing the sample and population is important because it helps us to understand the limitations of the sample and how it may not accurately represent the entire population. This can help us to make informed decisions and generalize the results to the entire population.

Q: What are some key differences between the sample and population?

A: Some key differences between the sample and population include:

Size: The sample is typically much smaller than the population.
Representation: The sample may not accurately represent the entire population.
Employee Sizes: The sample may have a limited range of employee sizes compared to the population.

Q: How can I increase the accuracy of my sample?

A: To increase the accuracy of your sample, you can:

Increase the sample size: A larger sample size can provide a more accurate representation of the population.
Use a more representative sample: A sample that is more representative of the population can provide a more accurate representation of the population.
Collect more data: Collecting more data on the population can provide a more accurate representation of the population.

Q: What are some common biases that can affect the sample?

A: Some common biases that can affect the sample include:

Selection bias: This occurs when the sample is not representative of the population.
Sampling bias: This occurs when the sample is not randomly selected from the population.
Non-response bias: This occurs when some individuals or items in the population do not respond to the survey or data collection.

Q: How can I avoid biases in my sample?

A: To avoid biases in your sample, you can:

Use a random sampling method: Random sampling can help to ensure that the sample is representative of the population.
Use a stratified sampling method: Stratified sampling can help to ensure that the sample is representative of the population by dividing the population into subgroups.
Use a weighting method: Weighting can help to ensure that the sample is representative of the population by adjusting the sample to match the population.

Q: What are some common mistakes to avoid when comparing the sample and population?

A: Some common mistakes to avoid when comparing the sample and population include:

Not accounting for biases: Failing to account for biases in the sample can lead to inaccurate conclusions.
Not using a representative sample: Failing to use a representative sample can lead to inaccurate conclusions.
Not collecting enough data: Failing to collect enough data on the population can lead to inaccurate conclusions.

Q: How can I ensure that my sample is representative of the population?

A: To ensure that your sample is representative of the population, you can:

Use a random sampling method: Random sampling can help to ensure that the sample is representative of the population.
Use a stratified sampling method: Stratified sampling can help to ensure that the sample is representative of the population by dividing the population into subgroups.
Use a weighting method: Weighting can help to ensure that the sample is representative of the population by adjusting the sample to match the population.

Q: What are some best practices for comparing the sample and population?

A: Some best practices for comparing the sample and population include:

Use a clear and concise methodology: A clear and concise methodology can help to ensure that the sample is representative of the population.
Use a representative sample: A representative sample can help to ensure that the sample is accurate and reliable.
Collect enough data: Collecting enough data on the population can help to ensure that the sample is accurate and reliable.

Q: How can I communicate the results of my sample to others?

A: To communicate the results of your sample to others, you can:

Use clear and concise language: Clear and concise language can help to ensure that the results are understood by others.
Use visual aids: Visual aids such as graphs and charts can help to illustrate the results.
Provide context: Providing context can help to ensure that the results are understood by others.

Q: What are some common challenges when comparing the sample and population?

A: Some common challenges when comparing the sample and population include:

Biases in the sample: Biases in the sample can lead to inaccurate conclusions.
Limited data: Limited data on the population can lead to inaccurate conclusions.
Complexity of the population: Complex populations can be difficult to analyze and may require specialized techniques.

Q: How can I overcome these challenges?

A: To overcome these challenges, you can:

Use specialized techniques: Specialized techniques such as stratified sampling and weighting can help to ensure that the sample is representative of the population.
Collect more data: Collecting more data on the population can help to ensure that the sample is accurate and reliable.
Use advanced statistical methods: Advanced statistical methods such as regression analysis and time series analysis can help to analyze complex populations.

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125

Business	Number of Employees
1	5
2	10
3	15
4	20
5	25
6	30
7	35
8	40
9	45
10	50
11	55
12	60
13	65
14	70
15	75
16	80
17	85
18	90
19	95
20	100
21	105
22	110
23	115
24	120
25	125