About Median in Math
What is Median?
The middle way or the center point of a group of numbers or data, in general, is known as the median of a group. When we have a series of numbers from the lowest order to the highest order, then the middle element of that series is the median.
The formula given here is applied to find the median of a given dataset:
How to Find the Median of some Data?
The student can find the median of data in multiple ways and these defined for a dataset containing an odd number of elements, and for a dataset with an even number of elements:
1. Odd-Numbered Data Elements
Go through the steps provided to find the median of an odd number of entries in a dataset:
Step 1: Arrange the given data in ascending order.
Step 2: Count the total number of elements in the series and find the middle element of the data.
Step 3: The median of the data is the middle element.
We have equation to find the median of a given data set: \(\frac{(n+1)}{2}\). Here n is the number of items in the data series and this equation to find the median is useful for an odd number of elements in a dataset.
2. Even Numbered Data Elements
Go through the steps below to find the median of an even number of elements in a dataset:
Step 1: Arrange the given data in ascending order.
Step 2: Count the total number of elements in the dataset and find the pair of the middle elements of the series.
Step 3: Calculate the average of the middle pair by adding both of the elements and dividing it by two.
Step 4: Now, the resultant number is the median of the given data set.
When we have a large set of elements in a dataset then students can use two formulas to simplify the question and the formulas are: \(\frac{n}{2} ~\text{and}~\left(\frac{ n}{2}\right)+1\)
Here n is the number of elements in the dataset and the results of the two formulas will give you the location of the middle pair of elements. After getting the middle pair add both the terms and divide it by \(2\).
The image below is an example of the median being obtained for the given data elements in first an odd set and then in an even-numbered dataset:
Solved Median Examples
Find the median of the given data in the following examples:
Odd-numbered data elements:
Example 1: Find the median of 15, 3, 9, 27, 38, 24, 26, 45, 56, 16, 21, 11, 55, 29, 22.
Solution:
- Arrange the given series of data elements into ascending order: 3, 9, 11, 15, 16, 21, 22, 24, 26, 27, 29, 38, 45, 55, 56.
- There are a total of 15 numbers, so the median or the center element is the eighth element: 24.
- Using the formula to find median of odd-numbered data elements is: \(\frac{(n + 1)}{ 2} =\frac{(15 + 1)}{ 2} = 8\)
Even-numbered data elements:
Example 2: Find the median of 12, 5, 9, 37, 22, 44, 32, 10, 25, 2.
Solution:
- Arrange the given series of data elements into ascending order: 2, 5, 9, 10, 12, 22, 25, 32, 37, 44.
- There are a total of 10 numbers, so the middle items are the fifth and sixth elements, or 12 and 22.
- Using the formula to find the median of even-numbered data elements is: \(\left(\frac{12}{2}\right)=6\) and \(\left(\frac{12}{2}\right)+1=7\)
- The average of the sixth and seventh elements is used to find the median. So by adding both of the elements and dividing it by two: \(\frac{(12+22)}{2}=17\)
Example 3: The table below displays the results of various players in a match. Find the mean, median, and mode?
Solution:
The mean of given data \(=\frac{(80 + 52 +40 + 52 + 70 + 1 + 6)}{7}\)
= 43
The mean of the series is 43.
Arrange the table in ascending order to calculate the median.
Median \( = \frac{(n + 1)}{ 2}\)
Median \( = \frac{(7 + 1)}{ 2} = 4\)
The median of given series: 52
Mode of the given data is 52.
Mean is the average of all the entities present in a list. The mean of some data is calculated by adding all the terms of the data and dividing it by the number of terms. The formula for mean is:
Mean \( =\frac{\text{Sum of the given element}}{\text{Total number of given data}}\)
When we have a set of data then the mode is the most frequently occurring element in the data.