Question

Discuss the advantages and disadvantages of all three measures of central tendency; mean, median, and mode. Give specific examples of situations in which you would find these measures useful.

Answer 1

Mean:

Advantages: Mean is the average of all the values in a dataset. It is a stable measure of central tendency and it is the commonly used measure of central tendency.

Disadvantages: Mean is affected by outlier , and changing one value (increasing or decreasing ) can change the mean

Example:

Let the numbers be : 3,7,8,12,13,17,22

Mean = 11.71429

So, it represents a good measure of the central tendency.

But, let the numbers be : 3,7,8,12,13,17,222

Mean= 40.2857

Clearly 222 seems like an outlier , so the mean 40.2857 doesnt represent the sample properly, since first 6 values are less than 40.

Median:

Advantages: Median is the middlemost value of a dataset , sorted in increasing order. It is the best measure where there are outlier in the data.

Disadvantages: Median just gives the middlemost value of the observation, it doesnt explain how many values in the dataset lies above or below that number.

Example :

Let the numbers be : 3,7,8,12,13,17,222

Median : Middlemost value = 12 (it represents the data properly, due to presence of outlier)

Let the numbers be : 3,3,3,3,3,5,6

Median : 3 ( whereas mean = 3.714 , so median only gives the value which doesnt explain the dataset properly, due to presence of other values like 5 and 6, here mean represents the sample better than median)

Mode:

Advantages : Mode is the value tat occurs maximum number of times in a dataset. It is the most easiest to calculate. It is best used in case of nominal dataset.

Disadvantages: It is not stable like mean, there can be multiple modes in a dataset.

Example: Lets consider a nominal data ,

Good, Bad, Ugly, Bad, Bad, Bad, Bad, Good, Ugly.

Here, Bad occurs maximum number of times here Bad is the mode, (here mean and median is undefined we cannot use it here)

Lets consider a data : 3,3,4,4,5,5

Mode=(3,4,5) (Clearly Mode is not well defined, Median =4 or mean = 4, so mean or median is well defined here )

Let the numbers be :