Question

First, what are the characteristics of a population for which it would be appropriate to use mean/median/mode? When would the characteristics of a population make them inappropriate to use

Answer 1

Mean:-

The mean (or average) is the most popular and well-known measure of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.

The mean is usually the best measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data is normally distributed. However, it all depends on what you are trying to show from your data.

Taking the median would be a better measure of central tendency if the outlier is present.

Another time when we usually prefer the median over the mean (or mode) is when our data is skewed.

The mean is generally an inappropriate measure of average for data that are measured on ordinal scales. Ordinal data are rated according to a category where a higher score indicates a higher or better rank than a lower score.

Median:-

The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution) or you are dealing with ordinal data. However, the mode can also be appropriate in these situations but is not as commonly used as the median.

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.

Mode

The mode is the least used of the measures of central tendency and can only be used when dealing with nominal data. For this reason, the mode will be the best measure of central tendency (as it is the only one appropriate to use) when dealing with nominal data. The mean and/or median are usually preferred when dealing with all other types of data, but this does not mean it is never used with these data types.

Conclusion:-

When you have a symmetrical distribution for continuous data, the mean, median, and mode are equal. In this case, analysts tend to use the mean because it includes all of the data in the calculations. However, if you have a skewed distribution, the median is often the best measure of central tendency.

When you have ordinal data, the median or mode is usually the best choice. For categorical data, you have to use the mode.