About Mean Vs Median
Mean
Mean can be defined as the average of a data set. We can also say that it is the sum of all elements in a data set divided by the total number of elements in a data set. The most common type of mean is the arithmetic mean.
Arithmetic mean \((\bar{x})~=~\frac{\text{Sum of all elements in a data set}}{\text{Total number of elements in a data set}}\)
\((\bar{x})\): It is used to denote the arithmetic mean.
For example, let us consider a sample set having n number of entities in the data set, that are: \(x_1,~x_2~,x_3,….~,x_n\)
Then the arithmetic mean, or simply mean, can be calculated by using the formula:
\(\bar{x}~=~\frac{x_1~+~x_2~+~x_3~+…..~+~x_n}{n}\)
where \(n\) represents the number of items in the data set.
Median
The median, on the other hand, is simply the number or value that lies in the middle of a data set.
The median can be calculated by arranging the data set in a specific order. They can be arranged in ascending or descending order. This is how you find the median for even and odd data sets:
- If the number of elements in a data set is even, the median can be calculated by taking the mean of the two middle numbers.
For example: If \(x_1,~x_2,~x_3,~x_4,~x_5,\) and \(x_6\) are arranged in ascending order, then:
Median \(=~\frac{x_3~+~x_4}{2}\)
- If the number of elements in a data set is odd, the median is the middle of the number in the data set.
For example: If \(x_1,~x_2,~x_3,~x_4,~x_5\) are arranged in ascending order then:
Median \(=~x_3\)
What is the difference between Mean and Median?
S.No | Mean | Median |
|---|---|---|
1 | The arithmetic average of all the elements of a data set is known as the mean. | The middle value of a data set when all the elements are arranged in order is known as the median. It is also used to separate the higher values from the lower values. |
2 | It is recommended not to use the mean for skewed data. | It is recommended to use the median for skewed data. |
3 | Mean is a type of arithmetic average. | Median is a type of positional average. |
4 | Mean is highly sensitive to outlier data. | Median is not very sensitive to outlier data. |
5 | The use of the mean can be limited due to external factors and errors caused by it. | Median is not very sensitive to outlier data. |
Solved Examples
Example 1: Find the median for the following data set:
2, 1, 8, 3, 9, 10.
Solution:
Given data: 2, 1, 8, 3, 9, 10
1, 2, 3, 8, 9, 10 Arrange the data in ascending order.
Number of elements = 6 (Even)
Median \(=~\frac{\text{Sum of middle data}}{2}\)
\(=~\frac{3~+~8}{2}\) Substitute
\(=~5.5\) Simplify
So, the median of the data is 11.5.
Example 2: Find the median for the following data set:
3, 11, 9, 5, 8.
Solution:
Given data 3, 11, 9, 5, 8
3, 5, 8, 9, 11 Order the data.
Number of elements = 5 (Odd)
Median = 8
So, the median of the data is 8.
Example 3. Find the mean of the following data sets:
2, 4, 3, 7, 1.
Solution:
Given data 2, 4, 3, 7, 1
Number of elements = 5
Mean \(=~\frac{\text{Sum of data}}{\text{Total number of data elements}}\)
\(=~\frac{2~+~4~+~3~+~7~+~1}{5}\) Substitute
\(=~\frac{17}{5}\)
\(=~3.4\) Simplify
So, the mean of the data is 3.4.
Example 4. Find the mean of the following data sets:
10, 0, 50, 30, 20.
Solution:
Given data 10, 0, 50, 30, 20
Number of elements = 5
Mean \(=~\frac{\text{Sum of data}}{\text{Total number of data elements}}\)
\(=~\frac{10~+~0~+~50~+~30~+~20}{5}\) Substitute
\(=~\frac{110}{5}\)
\(=~22\) Simplify
So, the mean of the data is 22.
A collection of related, discrete items of data that may be performed individually or in combination or managed as a whole entity is known as a data set. A data set is always organized in some type of data structure.
In statistics, the measure of center is a typical value for a probability distribution. The mean, the median, and the mode are the most common measures of center in statistics.
A mode is a value in the data set that appears most frequently. It is also said to be the most repeated value in a data set. A data set can have one mode, multiple modal values, or no mode.