Median, Mode, and Mean

The Mean, Median, and Mode as Measures of Central Tendency

The mean, commonly known as the average, is calculated by dividing the total number of values in a given data collection by the number of values (n). The median is the midpoint of a set of data that has been ordered either from smallest to largest or from largest to smallest. In contrast, mode refers to the value that appears the most frequently in a given data set. Under different circumstances, the mean, median, and mode are all reliable indicators of central tendency. For particular demographics, some become more appropriate than others. This essay explores the traits of a population for which the usage of mean, median, and mode would be most and least appropriate. The mean can be applied where the population data is either discrete or continuous data set (Laerd, 2017). However, most of the time the mean is used with continuous data. It gives the most common value in a data set. It is appropriate for populations that have no outliers since it reduces any errors in the prediction if the data set. It is the most commonly known measure of central tendency. However, is prone to the effect of the outliers. Outliers are the unusual values compared to the rest of the values in the data set (Laerd, 2017). Therefore, it is not appropriate for populations that have outliers. In such cases, the median is the best to use. In addition to that, populations with skewed data set make the use of mean inappropriate.

The Median: Appropriate for Skewed Data Sets and Odd Number of Values

The median works well when the number of values in the data set is an odd number (Laerd, 2017). For example, seven, nine, fifteen etc. It is appropriate where the given data set in population is skewed. However, it is not appropriate where the number of values in a data set are even, such as six, eight, sixteen etc. On the other hand, the mode works well where the population data is categorical and where we want to determine the most common category (Laerd, 2017). It is appropriate where the data set for a given population is skewed. It is inappropriate for population data set where the most common mark lies far much away from the other values in the population data set. In such cases, it does not give a very good measure of central tendency.

References

Laerd. (2017). Measures of Central Tendency. Retrieved from Laerd: https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php