What are the advantages and disadvantages of mean, median and mode?

The mean, median, and mode are all measures of central tendency used in statistics. Each of them has its own advantages and disadvantages, which I'll explain below: Mean: Advantages: It takes into account all the values in the data set and uses them to calculate the average, providing a comprehensive representation of the data. It is widely used in statistical analysis and is often used in inferential statistics. It is sensitive to every value in the data set, making it suitable for datasets with no outliers. Disadvantages: It can be greatly influenced by outliers, which can skew the value of the mean. It may not be a good representation of the data if the distribution is skewed or has extreme values. It requires interval or ratio level data to be meaningful. Median: Advantages: It is not affected by outliers, making it a robust measure of central tendency. It provides a value that is representative of the central position of the data, especially in skewed distributions. It can be used with ordinal, interval, or ratio level data. Disadvantages: It may not accurately represent the data if the distribution is multimodal or if there is a significant amount of missing data. It does not take into account the actual values of the data, only their position. It can be less precise compared to the mean when there is a large amount of data. Mode: Advantages: It is not affected by outliers and is useful in identifying the most frequently occurring value in a dataset. It can be used with nominal, ordinal, interval, or ratio level data. It provides a simple and straightforward measure of central tendency. Disadvantages: It may not exist if all values in the dataset occur at different frequencies, or if there are multiple values with the same highest frequency. It does not consider the actual values of the data, only their occurrence. It may not be a good representation of the data if the distribution is multimodal or if there is a wide range of values. It's important to note that the choice of which measure to use depends on the specific characteristics of the data and the goals of the analysis. In some cases, it may be beneficial to use a combination of these measures to gain a more complete understanding of the data.