Why do we use average? is there any limitations to their use ? illustr...
Why do we use average?
Average is a statistical measure that is widely used to summarize a set of data. It is a useful tool for researchers, analysts, and decision-makers to understand and interpret data. Average is used to describe the central tendency of a data set, which means it provides a single value that represents the whole set of data. It is used to make comparisons between different sets of data and draw meaningful conclusions.
Limitations of using averages
Although averages are widely used, there are some limitations to their use. It is important to be aware of these limitations when interpreting data and drawing conclusions.
- Outliers: Averages can be skewed by outliers, which are values that are significantly different from the rest of the data. Outliers can cause the average to be higher or lower than the true central tendency of the data.
- Sample size: The accuracy of the average depends on the sample size. A larger sample size tends to produce a more accurate average.
- Distribution of data: The distribution of data can affect the usefulness of averages. For example, if the data is highly skewed, the average may not accurately reflect the central tendency of the data.
Example of limitations of using averages
Suppose a company is interested in analyzing the salaries of its employees. The company has 100 employees, and their salaries range from $30,000 to $150,000 per year. The average salary of the employees is calculated to be $75,000 per year. However, this average may not accurately reflect the central tendency of the data because:
- There may be outliers, such as executives who earn significantly more than the rest of the employees, which could skew the average.
- The sample size of 100 employees may not be representative of the entire workforce, especially if there are significant differences between different departments or job roles.
- The distribution of salaries may not be normal, which could affect the usefulness of the average. For example, if most employees earn around $50,000 per year, but a small number of employees earn significantly more, the average salary of $75,000 per year may not accurately reflect the central tendency of the data.
Conclusion
In conclusion, averages are a useful tool for summarizing data and making comparisons. However, it is important to be aware of their limitations and to use them in conjunction with other statistical measures to gain a more complete understanding of the data.