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Introduction of Measures of central tendency: mean, median & mode

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Measures of central tendency are statistical metrics that describe the center or typical value of a dataset.
These measures give a single value that attempts to describe a set of data by identifying the central position within that set of data.
The three main measures of central tendency are the mean, median, and mode, each providing different insights depending on the nature and distribution of the data.

1. Mean

The mean, often referred to as the average, is calculated by adding up all the values in a dataset and then dividing by the number of values.
The formula for calculating the mean (xˉ) of a dataset (x1,x2,...,xn) of n numbers is:
The mean is a useful measure of central tendency when the data is relatively symmetrical and does not have outliers, as outliers can heavily skew the mean.

2. Median

The median is the middle value in a dataset when the values are arranged in ascending or descending order.
If there is an odd number of observations, the median is the middle number.
If there is an even number of observations, the median is the average of the two middle numbers.
The median is less affected by outliers and skewed data, making it a better measure of central tendency for skewed distributions.

3. Mode

The mode is the value that appears most frequently in a dataset.
There can be one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all if all values are unique.
The mode is particularly useful for categorical data where we want to know the most common category or value.

Choosing the Appropriate Measure

Mean is best when the data distribution is symmetric and there are no outliers.
Median is the preferred measure for skewed distributions or when the data contains outliers.
Mode is most useful for categorical data or to identify the most frequent values in a dataset.

Relation between Mean, Median, Mode

In biostatistics, the mean, median, and mode are measures of central tendency that describe different aspects of data distribution:

Mean is the average of all data points.
Median is the middle value when data is ordered.
Mode is the most frequently occurring value.

In a symmetric distribution, all three measures are equal. In skewed distributions, they differ, providing insights into data skewness and variability.

Mode ≈ 3 × Median – 2 × Mean