In statistics, median and average are two terms that are often used interchangeably. However, there is a big difference between the two measures. The Median is the middle value in a data set, while the average is the sum of all values divided by the number of values.
What Is Median?
The median is the value that separates the higher half of a data sample from the lower half. In other words, the value is halfway between the largest and smallest values in a data set. The median is often used as a measure of central tendency because it is not affected by outliers (extreme values that are far from the rest of the data).
What Is Average?
The average is the arithmetic mean of a set of numbers, the most common form of which is the arithmetic mean of a set of observations. It is defined as the sum of the numbers in the set divided by the number of items in the set. The arithmetic mean of a set of numbers x1, x2, …, xn is denoted by x̄ and is given by
x̄ = (x1 + x2 + … + xn)/n.
Key Differences Between Median And Average
- The Median is the number that divides a list of numbers into two equal parts. There are 2 medians if there are only two numbers.
- The Аverage is the sum of all the numbers divided by the number of numbers.
Median vs. Average Similarities
- Average: 50 – 50 is the range of numbers that fall in the middle of the group.
- Median: 50 – 50 is the middle number in a group of numbers.
- Lowest number: 19 – 19 is the lowest
Median vs. Average Pros and Cons
Median Pros & Cons
- The Median is less affected by outliers
- The Median does not rely on using quantiles or probabilities
- The Median is an excellent solution for highly skewed distributions
- The Median is easy to implement
- The Median is robust to outliers
- Median price can be misleading
- The median home price is compared to homes of comparable size, location, and construction
- The median price fluctuates significantly from season to season.
- The median home price doesn’t consider sales to first-time homebuyers
Average Pros & Cons
- Easy to find out, you just add up the figures in the set and divide it by the total count of figures in the set
- The Average is more affected by outliers
In closing, the average is the sum of all the values divided by the number of values. The median is the middle value that counts half as the first value and the other half as the second one. The average income of all Americans is $52,851, while the median wage is $31,660.