Question

Explain the following statement: "The median should always be used when a few very large or very small values affect estimates of the mean." Give examples of variables for which the median is typically used (8pts).

Answer 1

Answer:

We know that the arithmetic mean is not a good measure of central tendency when the data contains very large values or very small values such as outliers. These values affect the mean of the data and this mean is not a proper representative of the given data. We know that single outlier causes the shift of mean. So, to overcome this problem, we use median which is not affected by the extreme observations or values. The median is defined as the middle most observations of the data when data is an ascending or descending order. So, there is a very small role of extreme observations or outliers during the calculation of median.

Let us see the example of where median is typically used. During computation of income of persons from any region or state, median income is considered most of the time, because we know that there would be some outliers which could affect the mean income. The salary, grade, etc. are the examples where we use median.