Mean vs Median: How to Choose the Right Average

Introduction

In everyday language, the word “average” is usually associated with the arithmetic mean. However, in statistics, there are multiple measures of central tendency, with the mean and median being the two most widely used.

Choosing the wrong type of average can lead to distorted summaries and poor business or personal decisions, particularly when dealing with skewed data.

Head-to-Head Comparison

Feature	Arithmetic Mean (Mean)	Median
Definition	Sum of all values divided by count	The exact middle value of an ordered dataset
Sensitivity to Outliers	High (outliers drag the mean)	Low (outliers do not affect the median)
Mathematical Properties	Excellent (used in variance, standard deviation)	Limited (harder to use in complex algebra)
Best For	Symmetrical data (heights, test scores)	Skewed data (household income, house prices)
Calculation Speed	Fast (simple division)	Requires sorting data first

Mean Deep Dive

The arithmetic mean is the most common statistical average. It represents the point at which all values in a dataset are balanced.

Formula

For a dataset $X = {x_1, x_2, \dots, x_n}$, the mean ($\mu$ or $\bar{x}$) is calculated as: $$\mu = \frac{\sum_{i=1}^{n} x_i}{n}$$

Example

For a dataset of five monthly office expenses: $10, $20, $30, $40, $500 (where $500 is an outlier):

• Sum = $600
• Count = 5
• Mean = $600 / 5 = $120

Notice that the mean ($120) is higher than four out of the five data points. It does not represent a “typical” expense due to the single large outlier.

Median Deep Dive

The median is the physical middle point of a sorted dataset. Exactly 50% of the numbers in the set are smaller than or equal to the median, and 50% are greater than or equal to it.

How to Calculate

1. Sort the numbers in ascending order.
2. If the count $n$ is odd, the median is the value at position $(n+1)/2$.
3. If the count $n$ is even, the median is the average of the two middle numbers at positions $n/2$ and $(n/2)+1$.

Example

Using the same office expenses dataset: $10, $20, $30, $40, $500. The numbers are already sorted. Since the count is 5 (odd), the median is the middle number: $30.

This value ($30) is far more representative of a typical monthly expense for this office than the mean ($120).

When to Use Which

• Use the Mean when the data is roughly symmetrical and has no extreme values. Examples include human height, weights of manufactured goods, and standard test scores. The mean is also preferred when you need to calculate total sums or when performing advanced statistical tests.
• Use the Median when the dataset contains extreme outliers or is highly skewed. Classic examples include household income, home prices, and website loading times.

Vietnam Context

Statistical averages are vital in Vietnam’s rapidly growing market. For example, when looking at wages, the “average salary” reported for major cities is often skewed upwards by high earners in executive and technology roles. Looking at the median salary instead provides a more realistic picture of what a typical worker in Vietnam earns. Similarly, real estate prices in cities like Hanoi and Ho Chi Minh City are heavily skewed by high-end luxury developments; thus, median prices are much more representative of the market for middle-class homebuyers.