What are the advantages and disadvantages to each measure of central tendency?

Question

What will be an ideal response?

Answer 1

One of the advantages of the mode is that it is very simple to determine and appealing conceptually. It is the score or value that is the most frequent and that has the greatest probability of occurring in a distribution of scores. The mode is very easy for readers to comprehend and understand. The mode is also very simple to calculate. We just identify the score with the highest frequency (or proportion or percent) in either a tabular presentation of data or a graph (find the tallest or longest bar or the largest slice of pie). Finally, the mode is a very general measure of central tendency since it can be determined for variables measured at any level. The mode is an appropriate measure of central tendency for data measured at the nominal, ordinal, and interval/ratio levels. A disadvantage of the mode is that it does not take into account all or even most of the information available in a distribution. One thing statisticians do not like to do is ignore data or information, but that is exactly what the mode does; it ignores all information in the data except the values/scores with the highest frequency. By ignoring or throwing out information, the mode may at times give us a very misleading notion of the central tendency of our data. Because of this deficiency with the mode, when we have interval/ratio level data, we most often use an alternative measure of central tendency such as the median or the mean. The median has a number of advantages as a measure of central tendency. First, unlike the mode that can have more than one value, there will always be only one median. Second, as the score in the exact middle of a rank-ordered distribution of scores, the median value has intuitive appeal—it is easy to understand. Third, the median is a useful measure of central tendency that is used in some graphical displays of data. Finally, because the median does not use all of the scores in our data, it is not influenced by extremely high or extremely low scores. Even when there are outlying scores, then, the median is a very stable measure of central tendency, because it is defined as the 50th percentile and does not take the value of each and every score into account. One disadvantage of the median is that, like the mode, it uses only one or two pieces of information. The mean has a number of advantages as a measure of central tendency. First, it is intuitively appealing. Everyone is familiar with an average. The mean also uses all of the information in a data set, and this is an advantage as long as there are no outliers in the data. The mean is also an efficient measure of central tendency. In other words, if we had a population of scores (with a mean and median) and from this population, and we took many, many samples and calculated both the mean and the median for each sample, the medians of these samples would differ more from each other and the population median than the means would differ from each other and the population mean. The mean is the most efficient measure of central tendency. A disadvantage to the mean is that because it takes every score into account, the mean may be distorted by high or low outliers. When we sum every score to calculate the mean, we may at times be adding uncharacteristically high or uncharacteristically low scores. Sometimes, the mean can provide a distorted sense of the central tendency in our data. Since the mean uses every score in our distribution, high outliers can inflate the mean, and low outliers can deflate the mean, relative to what the value of the mean would be without the outliers.