Mean, Median and Mode

Measures of Central Tendency

A measure of central tendency is a point estimate (a single value) that represents the centre around which the majority of data values in a distribution cluster.
The three most commonly used measures to identify central tendency in medical statistics are the mean, median, and mode.

The mean, commonly known as the arithmetic average, is calculated by adding all the observed values in a dataset and dividing that sum by the total number of observations.
It utilizes every single data value in its calculation, making it a highly sensitive measure.
The mean is considered the best measure of central tendency for continuous variables that follow a symmetric or normal distribution.
Its major clinical limitation is that it is heavily distorted by extreme values (outliers) and skewed distributions, meaning it can sometimes provide a misleading representation of the data's center.

The median is the exact middle value of a dataset when all observations are arranged (ranked) in sequential order from the lowest to the highest.
If a dataset contains an odd number of observations, the median is the exact central value; if it contains an even number, the median is calculated as the average of the two central values.
It perfectly divides the dataset into two equal halves, corresponding exactly to the 50th percentile (or second quartile).
The median is the preferred measure of central tendency for skewed distributions because it is relatively insensitive to the presence of outliers.

The mode is defined as the most frequently occurring value within a set of observations.
Depending on the data, a dataset may have a single mode, multiple modes (referred to as bimodal or multimodal), or no mode at all if every value appears only once.
Unlike the mean, the mode is completely unaffected by extreme outlier values.
The mode is the most suitable measure of central tendency for describing categorical variables, particularly nominal data where calculating an average or ranking the data is impossible (e.g., blood groups).

The following table summarizes the high-yield differences between the three measures:

Feature	Mean	Median	Mode
Definition	The arithmetic average of all values.	The exact middle value of ranked data.	The most frequently occurring value.
Preferred Data Type	Normally distributed, continuous numerical data.	Skewed, continuous numerical data.	Categorical or nominal data.
Effect of Outliers	Heavily distorted and pulled towards the outlier.	Not significantly affected.	Not affected at all.
Information Utilization	Uses every single observation in its calculation.	Ignores most data points, focuses only on the center.	Ignores most data points, focuses solely on frequency.