In Statistics, the central tendency measures are namely Mean, Mode, and Median. We are using this central tendency to find the average value of the given set of numbers or data. Mean is used to find the average value of the given data. Mode is defined as repeated values of the given data.
The Median is defined as the middle value of the given data. In this article, we learn the definition of median, formulas, how to find the median, solved example problems on Median, advantages of the median, and disadvantages of the median, frequently asked questions on the median. Now, let us learn in detailed one of the measures called Median.
The median is different for different types of distribution. A median is a data or number that is separated by the higher half of a data sample, a probability distribution from the lower half. To find the median, first, the data should be arranged in order of greatest to the least value or least value to the greatest value.
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What is Median in Statistics?
In statistics, Median is the middle value of the given set of data, the data will be arranged in an order. The arranged data or observations can be either in descending order or ascending order.
Median is that the middle number during a sorted list of numbers. The median can be used to determine an approximate average, or mean, but is not be confused with the actual mean. If there is an odd number of data, the median value is the number that is in the middle, below, and above, or starting side and ending side have the same amount or the same size of data.
If there are even numbers of data or observations, then there is no single middle value, then the median is defined to be the middle two values are added and divided by 2. Consider an example of even numbers of data,
Example: Find the median of 2, 4, 6, 7
Solution: Given the data is 2, 4, 6, 7
Now we find the median of the data.
In even numbers of data, there is no middle value. So we can take the middle two values and then divided them by two.
Median = (4 + 6)/ 2 = 10 / 2 = 5.
Therefore, the median of given even data is 5.
Median Formula
To find the median of an odd number of data or observations and an even number of data or observations, we have different formulas. So it is necessary to recognize or identify first if we have the odd number of values or an even number of values in a given data set.
- If the total number of observations is even, then we have the formula to calculate the median. The formula is, Median = [{(n/2)}th term + {(n/2)+1}th term]/2 Where ‘n’ is the number of observations.
- If the total number of observations is odd, then we have the formula to calculate the Median. The formula is, Median = {(n+1)/2}thterm where ‘n’ is the number of observations.
How to find Median in Math?
The median can easily found, in some cases and don’t even require calculations. The steps of finding median are as below,
- Arrange the data in ascending order it means from the lowest to the highest value.
- Identifying the number whether it is an even or an odd number of values in the dataset.
- Based on the results of the previous step, further analysis may follow two distinct scenarios.
- If the dataset or given data contains an odd number of values, the median is a central value that will split the dataset into halves.
- If the dataset or given data contains an even number of values, then we can find the two central values that split the dataset into halves. Then, calculate the mean of the 2 central values. That mean value is the median of the dataset.
Advantages of Median
For calculating the median we have some advantages, few of advantages are given below:
- Median can be calculated in all distributions.
- Extreme values do not have any impact.
- Median can be approximately determined with the help of a graph.
- Median is simple to understand and easy to compute.
- It can be calculated even if the values of all observations are not known or the data has an open-ended class interval.
- It is most useful dealing with qualitative data.
Disadvantages of Median
Some of the disadvantages are also there for the median. The disadvantages of the median are:
- It ignores extreme values.
- It is not easy to arrange the data in order of magnitude when a large population is involved.
- Median usually not representative of all values in the distribution.
Example Problems on Median
Example 1:
Find the median of 13, 15, 17, 25, 39?
Solution:
Given the data set is 13, 15, 17, 25, 39
Now we find the median of the value. Before finding the median, first, determine the given data set is an even number or an odd number.
The given data is an odd number. So the median is the middle set of value,
Therefore, the median of the given data set is 17.
Example 2:
Find the median of 2, 3, 5, 6, 7, 8, 12?
Solution:
Given the data set is 2, 3, 5, 6, 7, 8, 12
Now we find the median of the value. Before finding the median, first, determine the given data set is an even number or an odd number.
The given data is an odd number. So the median is the middle set of value,
Therefore, the median of the given data set is 17.
Example 3:
Determine the median of 6, 8, 3, 7, 5?
Solution:
Given the data set is 6, 8, 3, 7, 5
Now identify the given data as odd data or even data.
The number of observations is odd, so the given data has 5 observations.
The number of observations is n, n = 5
Now arrange the given numbers in ascending order we get,
3, 5, 6, 7, 8
we know the formula, for calculating the median of odd observations is,
Median = {(n+1)/2}th term
Median = {(5+1)/2}th term
Median = (6/2) term
So, the 3rd term is 6.
Therefore, the median for the given dataset is 6.
Example 4:
John’s family went through seven different places tour. The price of entry tickets for zoo park differs from place to place. Calculate the median of the ticket cost.
10.79, 12.61, 20.09, 15.84, 19.96, 25.11, 16.75
Solution:
Given the data set is 10.79, 12.61, 20.09, 15.84, 19.96, 25.11, 16.75
Now arrange the given data in ascending order. we get
10.79, 12.61, 15.84, 16.75, 19. 96, 20.09, 25.11
The given data set is the odd number of observations. so the median is the middle of the data.
Therefore, the median of the given data set is 16.75
Example 5:
Determine the median of given even observations of data 2, 4, 6, 8, 11, 14?
Solution:
Given the even observation data set is 2, 4, 6, 8, 11, 14
Now arrange the given data in ascending order, but the given data is already in ascending order.
The number of observations, n = 6
We know the formula to calculate the median of even observations is
Median = [(n/2)th term + {(n/2)+1}th term]/2
Median = [(6/2)th term + {(6/2)+1}th term]/2
Median = (3rd term + 4th term)/2
Hence the 3rd term is 6 and the 4th term is 8
The median is = (6+8)/2
= 14/2 = 7
Therefore, the median of the given even data set is 7.
Simple Method for finding Mean without using Median
Given data is 2, 4, 6, 8, 11, 14
Now we find the median of the given data.
Before finding the median, you can arrange the given data in ascending order. But the given data is already in ascending order.
In median, we have an even number of observations, then find the mean of the middle two values.
We know the find the mean or take middle two values and sum is divided by two we get the median value.
Median = (6+ 8 )/ 2
Median = 14 / 2 = 7
Therefore, the given data set median is 7.
Frequently Asked Questions on Median
1. Is it better to use median or average?
Median is determined by ranking the data from largest to smallest and identifying the middle so that there is an equal number of data values larger and smaller than it is. Under these median gives a better representation of central tendency than average.
2. Define the Median?
In statistics, Median is the middle value of the given set of data, the data will be arranged in an order. The arranged data or observations can be either in descending order or ascending order.
3. List the advantages of Median?
1. Median can be calculated in all distributions.
2.Extreme values do not have any impact.
3. Median can be approximately determined with the help of a graph.
4. Median is easy to understand and easy to compute.
4. What is the rule of Median?
Arrange your numbers in numerical order. Count how many numbers you have. If you have an odd number, divide by 2 and the remaining middle data is to get the position of the median number. If you have an even number, take the middle numbers or data sum and divide by 2. The dividend result is the value of the even number median.
5. What are the properties of Median?
The properties of the median are,
- Median can be applicable for the ordinal level.
- It may not be an actual observation within the data set.
- It is not suffering from extreme values because the median may be a positional measure.
- Median exists in both quantitative data and qualitative data
6. Where the Median is used?
1. The exact midpoint of the data or value distribution is needed.
2. There extreme values or data in the distribution