What is the Median and How to Calculate It – One part of statistics that is quite fun to calculate is the median. Together with the mean and mode , the median enlivens the realm of statistics. This statistical trio is very popular in everyday life.
Before discussing more about the median, we must first know that the median is a part of the center of the data. What is the measure of the center of the data?
The measure of data concentration is a descriptive method that shows the center of a data or a representation of a data. There are three sizes of central data that we are familiar with, namely the mean, mode, and median. This paper will discuss the median.
Is it difficult to determine the median? Relatively difficult or easy, yes, but it does require god-level patience to work out the median. Not only that, accuracy is also needed.
One calculation can make the next step confusing. One number, all data wrong. It’s like a proverb because a drop of tilapia is damaged by a pot of milk
The teachers at school are very familiar with statistics, especially when they assess their students. Likewise, the researchers are really soulmate with this. They need to process the data that they have been getting up and down.
Want to try the fun of calculating the median? Come on, let’s slowly discuss this median.
A. Definition of Median
The median is the central number of a set in a measure of the center of the data. Where, arrange the data points from smallest to largest and find the center number. So that’s the median. However, if there are 2 numbers in the middle, the median is the average of the 2 numbers.
To further animate the median, consider the following illustration:
Even though the median is the middle value, that doesn’t mean that once we get the data, we immediately determine the data in the middle, it’s the median.
This illustration is clearly wrong. This is not the middle value rather it is the middle position. if we look at it, it will be wrong if the baby with the lowest weight among the others becomes the middle value, right?
The median is a datum that is located in the middle of a data set, but what are the conditions? The condition is that the data is sorted from smallest to largest. So once you get the data, you have to sort it first!
now the children are arranged so that they stand starting from the lowest weight to the highest. Through this illustration, we can immediately determine that the median is a child weighing 24 kg. This data has been sorted so that we can immediately point to the child in the middle weighing 24 kg.
So, in discussing the median, we can pay attention to the amount of data available, whether the data is odd or even. Finding the median of odd and even data will be different.
So once again, the main requirement for determining the median is to sort the data. Sort from the smallest value to the largest value.
Where the median is the middle value in a table list of numbers in ascending or descending order, and can be more descriptive than the mean or average value.
The median is often used as the opposite of the mean when there are outliers in the sequence that might distort the mean. The median of a data sequence can be less affected by outliers than the mean or average.
B. How to Find the Median
There are 2 types of data sought for the median, namely single data median and interval data median
1. Single data median
Single data is unit data. Single data is divided into 2, single odd data and single even data
Single data is data that is presented simply and the data has not been arranged or grouped into interval classes.
a. Odd single data
For an odd number of data, we can look directly at the data and take the middle number, make that easier? as long as it’s sorted of course.
If there are odd numbers, the median is the number in the middle, with the same number of numbers below and above.
Now the steps to determine the median odd value:
- Sort data data groups from the smallest value to the largest value or vice versa.
- Determine the middle value.
- The amount of data on the left and right sides must be the same so that there is one number right in the middle which is the median of the data group.
The formula for finding the median for single data is as follows:
Example Question 1:
Calculate the median from the following data: 9,1,3,7,5
discussion:
sort data from smallest to largest
1,3,5,7,9
1st data : 1
2nd data: 3 3rd
data: 5 4th
data: 7 5th
data: 9
second count the number data(n)
n = 5
Third enter in the formula
Me = X (n+1) / 2
Me = X ( 5+1) / 2
Me = X (6)/ 2
Me = X₃
the third data is 5, then the median is 5
Example question 2:
1, 2, 8, 11, 6, 10, and 16!
find the median of the data
. Discussion:
First , we sort
the data
from
the smallest
. -5:10 data 6:11 data 7:16
second, calculate the amount of data.
The amount of data = n = 7
third plug it into the
Median formula:
Me = X ( n+1)/2
Me = X ( 7+1)/2
Me = X (8)/2
Me = X₄
We see above that the 4th data is 8
So the median of the data is 8
Example question 3:
Find the Median of the data: 7, 8, 8, 9, 4, 3, 7, 9, 5, 7, 6, 5, 6. Let’s
first sort the data from smallest
3, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9
data 1st : 3
data 2nd: 4
data 3rd: 5
data 4th: 5
data 5th: 6
data 6th: 6
data 7th: 7th
data 8th: 7th
data 9th: 7th
10th: 8th data
11th : 8th
data 12th: 9
13th data: 9
So the total data is 13, yes
Me = X (13+1)/2
Me = X (14)/2
Me = 7th data.
We can see above that the 7th data is 7
, so the median data is 7.
b. Single even data
Meanwhile, for an even number of data, there will be 2 numbers in the middle. So in order for us to get the median value, we have to use a different formula than determining the median for odd single data.
If there is an even number of numbers in the list, the middle pair must be determined, added up, and divided by two to find the median.
The steps for determining the median for even single data are as follows:
Sort data groups from smallest to largest value or vice versa.
Determine the middle value. The amount of data The left and right sides must be the same. Leave the two numbers in the middle and then find the average
The following is the median formula for even data:
example question 1:
Calculate the median from the following data: 4,8,6,2
the first discussion,
we order the data from the smallest
data order: 2,4,6,8
1st data: 2
2nd data: 4
3rd data: 6
4th data: 8
second, calculate the amount of data.
The amount of data = n = 4
third plug it into the
Median formula:
Me = X n/2 + X (n/2 + 1 ) / 2
Me = X 4/2 + X (4/2 + 1 ) / 2
Me = X 2 + X (2+ 1 ) / 2
Me = (X ₂ + X₃ )/ 2
Me = (4 + 6) / 2
Me = 10/2
= 5
so the median of this data is 5
Example question 2:
If the following data are known:
1, 2, 8, 11, 6, 10, 12 and 16,
find the median of the data
Discussion:
first we sort the data from the smallest
data sequence: 1, 2, 6, 8, 10, 11, 12, 16
1st data : 1 2nd
data: 2
3rd data: 6
4th data : 8th
data 5th: 10th
data 6th: 11th
data 7th: 12th
data 8th: 16
then we enter it into the even data median formula
Me = (X n/2 + X (n/2 + 1 )) / 2
Me = (X 12/2 + X (12/2 + 1 )) / 2
Me = (X ₆+ X (6 + 1 )) / 2
Me = X ₆+ X₇ / 2
Me = 11 + 12 / 2
= 23/2
= 11.5
so the median is 11.5
Example question 3:
First, we first calculate the sum of all frequencies
f = 9 + 10+ 12+6+2+1 = 40
Me = (X n/2 + X (n/2 + 1 )) / 2
Me = (X 40/2 + X (40/2 + 1 )) / 2
Me = (X₂₀+ X (20 + 1 )) / 2
Me = X₂₀+ X₂₁ / 2
Me = X₂₀+ X₂₁
Now for the 20th and 21st data it turns out that it is located at the number of frequencies 31 alias the data is at frequency 12
both the 20th or 21st data are both 7.
Please have a look at the following table:
Me = 7+ 7
2
= 14
2
7
so the median is 7
In studying the median or other material, you must master the basic skills first. This Basic Mathematics book can help you to understand the foundation needed to develop your math skills.
2.2. Interval Data Median / Group Data
Grouped data is data that is usually presented in the form of a frequency table and the data has been arranged or grouped into interval classes
mathematically.
The median of interval data is formulated as follows:
Tb = bottom edge of median class – p
p = 0.5
n = sum of frequencies
f kum = number of frequencies before median class
fm = frequency before median class
If values are expressed in integers and p= 0.05 if values are expressed in decimal 1 number behind the comma.
confused huh? Calm down, let’s try using questions
A data collection was carried out by a group of researchers to find out the height of the 1st grade students. Calculate the mean from the data for the 1st grade students’ height group at Happy Always Elementary School if the following data is obtained:
First, we add up all the available frequencies.
The number of frequencies = 12 + 18 + 10 = 40
Second, determine the median class:
the median class is data that contains the n/2th
, then the media class = 40/2= 20
Let’s make a table…
The median class is indicated by the 20th data where it is located in the 2nd group at the 2nd frequency which totals the frequency is 30.
group: 2nd
interval: 120-130
at f before f median class = 12
frequency before median class (fkum)
fkum = 12
while the frequency where the median class is at fm
fm= 18
interval distance l = 10
Because the data is expressed in integers, the lower edge of the median class is as follows.
the lower value of the 3rd group
the interval 120 – 130
is 120
Tb = 120- p
because it is an integer then p = 0.5
Tb = 120 – 0.5 = 119.5
Thus, the median is formulated as follows.
Me = Tb+ [ ½ n- fkum] l / fm
Me = 119.5 + [ ½ 20-12 ]. 10/10
= 119.5 + [10 – 12 ,] 10 / 10
= 119.5 + (-2).10 / 10
= 119.5 – 20 / 10
= 119.5 – 2
= 117.5
So, the median of the data it is 117.5
Example question 2:
Determine the median of the following student height data.
First, because there is a lot more data than before, we take a deep breath first, after that we have counted a lot of data, you
can see from the frequency gaess
1st frequency : 6th
frequency 2nd frequency : 8th
frequency 3rd : 10th
frequency 4th : 5th
frequency 5th : 4th
frequency 1st : 3rd
Let’s add up
Total (n)=6 + 8 + 10 + 5 + 4 + 3 = 36
So after that, let’s determine the median class, the
median class is the data that contains n/2
, so the Median class = 36/2 = 18
Observe the following table:
The median class is indicated by the 18th data where it is located at:
3rd group
Interval 150-154
at f before f median class = 8
frequency before median class (fkum)
fkum = 14
while the frequency where the median class is at fm fm
= 10
interval distance l = 5
Because the data is expressed in integers, the lower edge of the median class is as follows.
the lower value of the 3rd group
the interval 150 – 154
is 150
Tb = 150- p
because it is an integer then p = 0.5
Tb = 150 – 0.5 = 149.5
Thus, the median is formulated as follows.
Me = Tb+ [ ½ n- fkum] l / 10
Me = 149.5 + [ ½ 36- 14 ]. 5 / 10
= 149.5 + [18 – 14 ,] 5 / 10
= 149.5 + (4).5 / 10
= 149.5 + 20 / 10
= 149.5 + 2
= 151.5
So, the median of these data is 151.5
Darmawati’s Sensible Book of SMA/MA Mathematics Questions for Class X, XI and XII can help Sinaumed’s to practice their math skills through various practice questions in it.
So, what about the median questions given along with the discussion, have you got enlightenment?
The advantage of the median is that it is easy to calculate if the amount of data is relatively small. So if the amount of data is small, it’s really easy.
But the title is different if the data provided is a lot. Of course it takes extra effort that makes us sweat from all directions.
While the drawback of the median is that the median value is relatively unstable even for data in the same population. However, the median is a part of basic statistics that must be understood.
The function of the median is to measure the concentration of land. In statistics and probability theory, the median is the value that separates the higher half from the lower half of a data sample, population, or probability distribution.
The advantages of the median are firstly that it is not used for extreme data, secondly it can be used for both quantitative and qualitative data and thirdly it is very suitable for heterogeneous data.
Meanwhile, the weaknesses are the first that it does not consider all data values, the second is that it cannot describe the average population, and the third is sensitive to the amount of data.
That’s a brief explanation of the median that you can find out. Hopefully it will be a little enlightenment for those of you who are studying statistics. Hope it is useful.