Mean
A set of values is called the mean when its sum is divided by the total count. It offers a balancing point by presenting the data’s general trend (Yadav et al., 2019). However, a single extreme value might drastically distort the outcome because the mean is highly susceptible to outliers. In a household income dataset, for example, the income of a billionaire would disproportionately affect the mean, making it less representative of the majority.
Median
In contrast, the midpoint of a data set, in ascending or descending order, is known as the median. Because it is less susceptible to extreme values, it is a reliable indicator of central tendency. However, when the dataset is skewed, the median may be more accurate at representing the overall distribution (Fabián, 2021). For example, given a wage dataset in which the majority earn $50,000, but the minority earn $200,000, it would be more accurate to use the median as a measure of regular income.
Mode
The value that appears the most frequently in the dataset is the mode. Although it provides information on the most common result, datasets without repeated values or with several modes might not be able to use it (Beyer, 2021). For example, in a study of people’s favorite ice cream flavors, vanilla might be the most popular; however, if two or more varieties are equally popular, there won’t be a mode.
Choosing an Optimal Central Tendency Measure
The advantage of the mean is that it is easy to compute, but its sensitivity to outliers can be a big drawback. While the median’s resilience to outliers is advantageous, it has the disadvantage of providing a less precise representation of the overall trend (Fabián, 2021). Although the mode is effective for categorical data, it may not be effective for continuous data.
The selection of the most appropriate central tendency measure depends on the dataset’s characteristics and the investigation’s objectives. In symmetric datasets with few outliers, the mean gives a broad picture. The median is frequently more trustworthy when working with skewed or outlier-prone datasets. In conclusion, the features of the available data must be considered when selecting the best measure of central tendency, and careful evaluation of each measure’s benefits and drawbacks is essential for reliable statistical analysis.
References
Beyer, A. (2021). Measures of central tendency. Introduction to Statistics for Psychology.
Fabián, Z. (2021). Mean, mode or median? The score mean. Communications in Statistics-Theory and Methods, 50(10), 2360-2370.
Yadav, S. K., Singh, S., Gupta, R., Yadav, S. K., Singh, S., & Gupta, R. (2019). Measures of central tendency. Biomedical Statistics: A Beginner’s Guide, 41-52.