Question

In statistics, there are several common measures of central tendency of a distribution of values, including the arithmetic mean, the median and the mode. Under what circumstances would it be better to use the median instead of the arithmetic mean? And why would the arithmetic mean be misleading? Please cite examples.

Answer 1

1) If data set contains the outliers then median is better than mean. Example, consider the data set 2,5,7,11,100 here, the observation 100 is an outlier if we calculate mean of this data set it gives mean value 25, all the observations except the outlier are less than mean value which gives misleading result. But if we calculate median of data set , which is middle most observation, it is 7. Which is better than the mean. 2) For a continuous frequency distribution having Open- end class we cannot calculate mean , but median can be evaluated.