He task is a Applied statistics assignment.
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?
Applied statistics
Question: 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 inappropriate to use?
Statistics is something that surrounds us in every thing that we do. Therefore, understanding the different forms of statistics and there use is essential to be able to distinguish between these that are used properly and those misused or aimed at deceiving. Mean, mode and median are the measures of central tendency that helps in description of set of data by help in to identify the central position with a given data set. This paper therefore provides a number of characteristics in a population that makes it appropriate to use mean. Mode and median as well other those characteristics that would render the population inappropriate to use these measures of central tendency.
One of the characteristics of the population that requires use of mean, mode and median is large population. A larger population becomes difficult to make sense out of it. Such population requires to be consolidated and synthesized to help enhance understand the useful and enlightening indicators (EDL. 2014). For example, when given a population of 1000, it becomes very easy to understand the data using these measures of central tendency. For instance, mean which is arrived at by finding the average of the entire population helps to enhance understanding where the majority of the population falls. Therefore, it becomes a little bit easier to analyze information and to understand as well. Median is the middle number in a population. This figure is also important in helping to understand the middle number in a population. Mode on the other hand, is the number that appears more than others do. This is also important in gaining an understanding about the data.
Another characteristic of the population is whether it is continuous or not. The population that is best to use mean, median and mode is continuous (Chu-Carroll, 2007). Mean is effective and recommended to describe numerical data that is normally distributed. It is therefore sensitive to extreme values in data set. Therefore, for the mean to be effective, the population must be systematic and normally distributed. This will eliminate the problem of extreme values.
Another characteristic of the population that makes it appropriate to use median is that the data is ordinal and non-numerical. This becomes essential if the population has some differences as well as abnormally distributed figures (Guo & Bollen, 2013). For instance if the data sets vary and are extreme, this measure is appropriate because it helps in location of the middle or the center of the general data set. Mode is also applicable and appropriate and can be used when the population is bimodal. The data set may have various sets of data making it have more than two modes. Therefore, in such circumstances, it becomes an important measure to help in identifying and describing the data sets in a population that are equal.
For extreme populations it is not appropriate to use mean. This is because; the mean will not be representative of the population. For example, when the data set are ( 2. ,3,,4,5,5,20), the data set 20 is extreme and this will affected The mean making the figure fail to accurately describe the distribution of the population. Therefore, because of this outlier, the true center of the data will not be resented accurately.
In conclusion, various characteristics of the population need to be factored in when making a decision to use measures of central tendency. It is important to understand that certain attributes of the population deter the application of these measures of central tendency and should not be used. Mean, mode and media are very essential when the information is to be condensed or synthesized. It therefore makes it easier to understand the trends in larger populations.
References
EDL. (2014). Lesson 1: measures of central tendency