Shortcomings of measures of central tendency
Mean
The mean, or average, is the most commonly used measure of central tendency. However, it has a number of shortcomings, including:
- It is sensitive to outliers. A single outlier can have a significant impact on the mean, making it a misleading measure of central tendency for skewed data.
- It does not take into account the distribution of the data. Two datasets can have the same mean, but very different distributions. This can make it difficult to compare datasets using the mean.
- It is not always easy to interpret. For example, if the mean income in a city is $50,000, does this mean that everyone in the city earns $50,000? No, it is likely that some people earn much more than $50,000, while others earn much less.
Median
The median is the middle value in a dataset when the values are arranged in order of magnitude. It is less sensitive to outliers than the mean, and it is a more accurate measure of central tendency for skewed data. However, the median also has a number of shortcomings, including:
- It does not take into account all of the values in the dataset. For example, if the median income in a city is $50,000, this does not mean that everyone in the city earns $50,000 or more.
- It can be difficult to calculate, especially for large datasets.
- It is not always easy to interpret. For example, if the median income in a city is $50,000, does this mean that half of the people in the city earn $50,000 or more? Not necessarily.
Mode
The mode is the most frequent value in a dataset. It is the easiest measure of central tendency to calculate, and it is a good measure of central tendency for categorical data. However, the mode also has a number of shortcomings, including:
- It is not always a meaningful measure of central tendency. For example, if the most common age in a group of students is 18, does this mean that the average student is 18 years old? Not necessarily.
- It is not sensitive to the distribution of the data. Two datasets can have the same mode, but very different distributions. This can make it difficult to compare datasets using the mode.
- It is not always unique. A dataset can have more than one mode.
Example from the media
In a recent article, a news organization reported that the average salary for software engineers in the United States is $110,000. The article used a mean salary to calculate this average. However, it is important to note that the distribution of salaries for software engineers is skewed, with a small number of engineers earning very high salaries. This means that the mean salary is likely to be inflated by the salaries of these high-earning engineers.
A more accurate measure of central tendency for software engineer salaries would be the median salary. The median salary for software engineers is $95,000. This means that half of all software engineers earn $95,000 or more, and the other half earn less than $95,000.
Evaluation
The news organization used the wrong measure of central tendency to report the average salary for software engineers. The mean salary is not an accurate measure of central tendency for skewed data. The median salary would be a more accurate measure of central tendency in this case.
Recommendation
The news organization should use the median salary to report the average salary for software engineers. The median salary is a more accurate measure of central tendency for skewed data.
Conclusion
It is important to be aware of the shortcomings of measures of central tendency when using them to describe data. The mean, median, and mode all have their own strengths and weaknesses. It is important to choose the right measure of central tendency for the data you are using and to be aware of the limitations of that measure.
