Mean is what most people call it as an average. It is calculated by adding all the numbers in a data set and then dividing by the number of observations (numbers).
Example : Let's say you have the following dataset containing five values.
| Values |
|---|
| 5 |
| 10 |
| 11 |
| 12 |
| 15 |
Calculation : Sum of all these five numbers are 53. Since these are 5 values so mean is 53/5 i.e. 10.6.
Median is the middle value in a dataset. It is calculated by sorting observations from smallest to largest and checking the middle value.
The median of the following dataset is 11 which is the middle value.
5, 10, 11, 12, 15
When to Use Mean
Mean is more appropriate when the dataset does not contain outliers (extreme values) and it is evenly distributed.
Example : Suppose you have a group of 5 friends and their ages are 25, 26, 27, 28 and 29 years.
Mean Age : Sum up all the ages and divide by the number of friends. (25+26+27+28+29)/5 = 27. Mean age is 27 years.
Median Age : Arrange the ages from smallest to largest (25, 26, 27, 28, 29) and select the middle one. The median age is also 27 years.
In this example, both the mean and median accurately represent the data because it does not contain any outliers.
When to Use Median
Median is more appropriate when the dataset contains outliers (extreme values) and the distribution of dataset is skewed.
Example : Let's say a company where employees have these salaries : $30,000, $40,000, $50,000, $60,000 and $500,000.
Mean Salary : You add up all the salaries and divide by the number of employees. (30,000+40,000+50,000+60,000+500,000)/5 = $136,000. Mean or average salary is $136,000. It doesn't accurately represent what most people in the company earn because it’s skewed by the CEO's high salary.
Median Salary : Arrange salaries in ascending order ($30,000, $40,000, $50,000, $60,000 and $500,000) and select the middle value. The median salary is $50,000. It accurately represents what most employee earn in the company.
In this example, the median gives a better sense of the data while the mean is skewed by the very high salary of CEO.
Lies in Numbers: Mean and Median Examples
Here are some examples where people misuse statistics like mean and median to manipulate perceptions.
- Average Home Price : You may have seen advertisement "Average home price in our neighborhood is $500,000". This sounds impressive but if the distribution is skewed with a few luxury homes, the median price could be much lower like $300,000.
- Placement Statistics : Some colleges say the average starting salary is $80,000. But that number can be misleading because most graduates get around $60,000. A small number of high salaries like more than $150,000 push the average to $80,000. In truth, a better picture is shown by the median salary which is $60,000.
Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. He has over 10 years of experience in data science. During his tenure, he worked with global clients in various domains like Banking, Insurance, Private Equity, Telecom and HR.
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