Population Characteristics

Mean, mode, and median are measures o central tendency which describe the average of a normal data distribution. The three measures are commonly used to describe a distribution, though they are used under certain conditions to best represent the data – and this indicates that if some conditions are not met for a distribution using the wrong measure would lead to misleading description about that distribution. The mode is described as the most occurring number or the value appearing with the greatest frequency over the other values. The use of mode is appropriate for data having several values appearing more than once, as well as, for nominal data unlike mean and median (Bryman, 2016). Ideally, with nominal data – data without numerical values – the use of mode is appropriate as it would communicate the categorical name appearing the most times. For example, taking a sample of Japanese family names, mode can be used to describe such data – the most appearing name.

            Mean reflects the sum of all the values in a distribution divided by the number of values in that distribution. For instance, mean is used appropriately in describing data distribution that is measure using ratio of interval scale but not skewed. Skewness indicates that data values are concentrated on either tail of a distribution (Little, 2017). For example, it would be appropriate to describe human heights in population using mean as it follows a normal distribution. However, it would be inappropriate to describe the salaries of different individuals working in different sectors where some may have as low as $5,000 while others have as high as $1 million. Also, it is inappropriate to describe distribution which is measured categorically such as names of individuals.

            Lastly, median indicates the middle number or value in a distribution when arrange in an ascending order. Ideally, it is used with distributions which can be measured by either ratio and interval scales and is skewed – more values are stretching on one tail of the distribution. It is inappropriate to describe categorical data such as names of people using median since one cannot arrange the names, numerically (Little, 2017). The median is less affected but skewness and outliers and this makes it a good measure of central tendency to describe data with outliers such as the US household income which in most cases is skewed to the left. 

References

Bryman, A. (2016). Social research methods. Oxford: Oxford University Press.

Little, D. (2017). Measures of central tendency: Mean, median & mode. Australia : University of Melbourne