The main difference between median and average is that the median refers to the middle value in a set of numbers, while the average of a set of numbers is the typical or central value.
Table of Contents
Median vs Average
| Median | vs | Average |
| It is the middle value of the series. | Definition | It is the sum of all entries in a group of numbers divided by the overall integers. |
| Positional average | Statistical Value | Arithmetic average |
| Depends on the total number of values | Outline | Depends on values |
| Higher the number more the mean | Change Frequency | Number does not affect median |
| Median involves arranging series in order and then determining the number that comes in the middle. | Value’s Position | Calculating the average involves adding or piling up all the data in the provided data set and then dividing the result by the sample’s total number of observations. |
Difference Between Median and Average
Definition
The median is the numerical number that appears in the center of an ordered list of numbers that is either ascending or descending.
Mean is the average or simple arithmetic mean of the specified collection of data, quantities, or ratings.
Statistical Value
The location of the data set will assist in determining the median’s value even though, the mean is the arithmetic average of a set of numbers, and the median is the positional average.
While the median will emphasize the sample or data set’s midway value, the mean will highlight the data set or sample’s center of gravity.
Remember that the mean is acceptable for regularly distributed data. On the other hand, in the case of skew data set, sample, or distribution, the median is more appropriate and the best choice.
Change Frequency
The outlier or the high value is significant and impacts the mean, but not the median.
Value’s Position
Calculating the average involves adding or piling up all the data in the provided data set and dividing the result by the sample’s total number of observations. The result is the mean.
On the other hand, the number of numbers or the selection will be ordered in either descending or ascending order, with the number corresponding to the precise midpoint or the sample’s center designated as the median.
Calculating Average and Median
A mean is the arithmetical average of a collection of two or more numerical values. It is also called the basic arithmetic average.
Different Approaches to Calculating the Mean
There are several ways to calculate the mean for any given group of numbers, including the arithmetic mean approach, which employs the sum of the numbers in the sequence, and the geometric mean approach.
Median Definition
The middle number in a list of such numbers is the median. You must first order the numerical values in value order, from least to highest, or else in ascending order, to get the median number in the series of numbers.
The median value, which is mathematical and is in the center with the same number of numerals above and below, is numerical if there is an odd number.
Finding the Median
Suppose the list has an equal number of items.
Step 1: First identify the middle pair.
Step 2: Add the two numbers together.
Step 3: Then calculate the median value by dividing the sum by two.
You may use it to estimate the mean or average.
However, sometimes data values include outliers in the sequence that might cause the average values to be skewed. The median is occasionally employed instead of the average or mean. In contrast to the standard or average, the median of a series may be less impacted by such outliers.
Examples
Average
Calculate the average and median for the series: 3, 5, 4, 1, 8, 9, 6
Here, the total observations are 7, and the sum of these observations is 36. So the average of this series is 36/7 = 5.14
Median
Step 1: To get the median, arrange them in order. The series would look like 1, 3, 4, 5, 6, 8, 9.
There are seven numbers.
Step 2: Using the formula, determine the n+1 position where n is the entire observation. This equals 8.
Step 3: Divide it by 2. The answer comes at 4. This means that the 4th observation, which is 5, is the median of this series.
The mean would be 5.14, and the median is 5.
Knowing the Difference Between Median and Average
Average and median are the two most simple yet crucial components of statistics in mathematics. They form a base for further analysis of the set of values in any given question.
Knowing the difference will enhance your understanding of these concepts and give you a clearer picture of statistics.