Particularly statistics is a branch of mathematics that helps to find the central tendency of the gathered data sample by using mean, mode, median. However, when a data sample is collected, data values in the gathered sample are arranged either in ascending order or descending order then the middle value of the given list of data is the median in statistics.
For example: Consider the list of data values and find the median – 6,2,8,3,1,5,4
Arrange the list in ascending order or descending order – 1,2,3,4,5,6,8
Middle number in the arranged list is considered to be the median.
So,4 is the median in a given list.
What is Median?
Let’s see another example to understand what is median. Suppose you have a series of numbers. To find the median you have to arrange them in an order (increasing or decreasing).
Given series – 78, 23, 76, 34, 94, 12, 48
When arranged in ascending order – 12, 23, 34, 48, 76, 78, 94
As 48 is the middle value of this series, this is the median.
So a median is the mid value of the data when arranged in an order which can be ascending or descending.
Median is also considered to be a kind of average to find the middle value of the given list of data. Hence, the median also determines the central tendency. Mode and mean also determine the central tendency apart from the median. Mode is the value in the given list of numbers which is repeated most of the time.
Mean is the average value that is obtained by adding the numbers in a list divided by the number of values in the list.In a set of data the middle or center value or halfway is considered to be the median.To find median, the data is arranged first either in ascending order or descending order the center value in arranged set is considered to be median.The median differs for different types of distribution.
Median Formula for Odd Set of Observations
There are two different formulas to find the median depending on whether the given set of data has an even or odd set of numbers.
- For eg: Consider the data set 1,3,5,8,9 and determine median.
- Here 5 is considered to be median since 5 is the middle number of the given set.
- This is calculated using the median formula for odd numbers – ((n + 1)/2)th term is the median.
- Applying the same here, median = (5 +1)/2 = 6/2 = 3rd term that is 5.
Median Formula for Even Set of Numbers
- Suppose 1,3,4,6,8,9 is a given set then there is no single middle number.
- Then median is the mean of the 2 middle values. So median = 4+6/2=5
- The median formula for even numbers used here is : ((n/2)th term + ((n/2) +1)th term )/2).
- Applying the same = (6/2 + (6/2) +1)/2 = (3rd number + 4th number)/2 = (4 +6)/2 = 10/2 = 5
What is Statistics?
Statistics is the study and manipulation of the data by gathering, reviewing, analysing and concluding the data sample. You can categorise statistics into 2 groups which are named as Descriptive statistics and inferential statistics. Statistics can be used to make investing decisions. Statistics can be used virtually in all scientific fields, as well as in business, humanities, government and manufacturing. Statistics is a branch of applied mathematics that is developed from application of mathematical tools including calculus and linear algebra to probability theory. The three important topics in statistics are mean, median and mode. This is a vast topic and needs to be practiced before you get a hang of it. You can visit online platforms like cuemath to understand this in a better way from subject experts who love Maths and teaching the same.