The Differences Between Median and Average
When it comes to statistical analysis, you’ll often hear two terms: median and average being used interchangeably. But, despite their similarities, they represent two different measures of central tendency. Here’s what you need to know about the differences between median and average:
What is Median?
The median can be defined as the middle value in a given set of data when arranged in ascending or descending order. In other words, when the data is divided into two equal parts, the median represents the value that lies at the center. It’s crucial to note that the median is not affected by the extreme values in the data set, i.e., outliers.
For instance, suppose we have the following data set: 2, 5, 7, 8, 9, 12, 16, 18. The median here will be 8 as it represents the value lying in the middle when arranged, and neither the high value nor the low value makes a difference.
What is Average?
The average, sometimes referred to as the arithmetic mean, is the sum of all values divided by the total size of the data set. In simple terms, it’s the value obtained when you add all the numbers in the data set and divide them by the number of items.
For instance, if we take the same data set mentioned above and find the average, we will first add all the values (2+5+7+8+9+12+16+18) which amounts to 77. To obtain the average, divide this sum (77) by the total number of items (8), which amounts to 9.625.
The Key Differences
The crucial difference between median and average is that the median divides the data set into two equal parts: half the values are less than the median, and half the values are greater than the median. On the other hand, the average is a representative value that gives an overall picture of the data set.
Another significant difference is that the median is not influenced by extreme values, whereas the average is susceptible to outliers. Therefore, the median is a better indicator of central tendency when there are outliers or skewed distribution in the data set.
In conclusion, both median and average are essential measures of central tendency, but they should be used accordingly in different scenarios. Understanding the difference and when to use which is critical when it comes to making informed decisions.
Table difference between median and average
| Median | Average | |
|---|---|---|
| Definition | The middle value in a set of data when arranged in order | The sum of all values divided by the number of values |
| Outliers | Not affected by extreme values | Can be heavily influenced by extreme values |
| Use | Used to measure central tendency when data has extreme values or is not normally distributed | Used to measure central tendency when data is normally distributed |