Comparison between Mean, Median, and Mode

The decision of which approach to employ for a particular collection of data depends on a number of factors that can be grouped into the following major categories:

1. Rigidly Defined: Mean and median are defined rigidly; on the other hand, mode is not always rigidly defined.

2. Based on all Observations: A suitable average should be calculated based on all observations. This attribute is only met by mean and not by median or mode.

3. Possess Sampling Stability: Mean should be preferred when the criteria of least sampling variability is to be attained.

4. Additional Algebraic Treatment: It should be able to get additional mathematical treatment. This attribute can only be satisfied by the mean, hence the majority of statistical theories utilise the mean as a measure of central tendency.

5. Simple to Calculate and Understand: It should be simple to understand and interpret an average. All three averages; i.e., mean, median, and mode satisfy this attribute.

6. Not significantly Impacted by Extreme Values: The appropriate average shouldn’t be significantly impacted by extreme observations. From this perspective, the mode acts as the most appropriate average. The existence of extreme observations has a very small effect on the median but a large impact on the mean.

A single value used to symbolise a whole set of data is called the Measure of Central Tendency. In comparison to other values, it is a typical value to which the majority of observations are closer. Average and Measure of Location are other names for the Measure of Central Tendency. In statistical analysis, the three principal measurements used in central tendency are Arithmetic Mean, Median, and Mode.

What is Mean?

Arithmetic Mean is one approach to measure central tendency in statistics. This measure of central tendency involves the condensation of a huge amount of data to a single value.

What is Median?

The positional value of a variable known as the median distributes the distribution into two parts that are equal; i.e., values above or equal to the median value are included in the first part, while all values below or equal to the median are included in the second part.

What is Mode?

Mode refers to the variable that occurs most of the time in the given series. In simple words, mode is a variable that repeats itself most frequently in a given series of variables (say, X). Mode is denoted as ‘Z‘.