Median

Introduction: Median

The median is a measure of central tendency that represents the midpoint of a dataset. It is particularly useful when data include outliers or are skewed, as it provides a more reliable indication of a “typical” value compared to the mean.

Background

As one of the three main measures of central tendency—alongside the mean and mode—the median is widely used in statistics and data analysis. Its robustness against extreme values makes it essential in fields where distributions are often uneven, such as economics and social sciences.

Key Elements / Features

To calculate the median:

1. Sort the data in ascending order.
2. Identify the middle point:
   • If the number of values is odd, the median is the middle observation.
   • If the number of values is even, the median is the average of the two middle observations.

Advantages of the median:

• Resilient to outliers – not distorted by extreme values.
• Representative in skewed data – gives a clearer picture of the central tendency in asymmetric distributions.

Applications / Examples

The median is widely applied across disciplines:

• Economics – Median income highlights typical earnings and reflects inequality better than the mean.
• Real estate – Median house prices show the central market value, unaffected by very high or low transactions.
• Social research – Summarising demographic data or survey results where distributions are skewed.

Example:
Suppose we have the dataset:

5, 7, 8, 12, 15, 18, 50

1. Ordered data is already listed.
2. The dataset has 7 values (odd number).
3. The middle value is the 4th element → 12.

So the median = 12.

Now consider an even-sized dataset:

3, 5, 8, 12, 14, 2

• There are 6 values (even number).
• The two middle values are 8 and 12.
• Median = (8+12) / 2 = 10.

Relevance / Impact

The median is a valuable statistical tool for describing central tendency, especially when datasets are non-normal or contain outliers. Its resistance to distortion makes it one of the most reliable indicators for decision-making, reporting, and policy analysis.

See also

• Mean
• Mode
• Quartiles
• Box Plot