Find Median of Grouped And UnGrouped Data

What is Median ?

        Median is a middle value in the given sorted data. It may be ascending or descending That is called Median.

Median In Un-Grouped Data

        In Un-Grouped data we have more two categories. 

        i.     Even

        ii.    Odd

       Even

            If our observed data is even, than we need to add both center values. 

            Formula: 

Median of Ungrouped Data Formula of Even Number

        Odd

            If our Observed data is odd we simply put the middle Number on the Array. 

            Formula:

Median of Ungrouped Data Formula of Odd Number

Median In Group Data 

        In this method we have given class intervals and frequency we simply solve this using formula.

        Formula:

Formula of Median in grouped Data

Median of Un-Group Data Code / Program in C /C++

#include<iostream>

using namespace std;

int main(){

int num;

float x[10],sum=0,mean,temp[10],Oloc,Eloc;

cout<<"Enter Total Number ";

cin>>num;

cout<<"X"<<endl;

for(int i=0;i<num;i++){

cin>>x[i];

}

cout<<" Given Data is: ";

for(int i=0;i<num;i++){

cout<<x[i]<<", ";

}

for(int i=0;i<num;i++){

for(int j=i+1;j<num;j++){

if(x[i]>x[j]){

temp[i]=x[i];

x[i]=x[j];

x[j]=temp[i];

}

}

}

cout<<endl<<" Arange : ";

for(int i=0;i<num;i++){

cout<<x[i]<<", ";

}

cout<<endl;

if(num % 2 == 1){

Oloc=x[num/2];

cout<<" Median of Odd Data is "<<Oloc;

}

else{

Eloc=(x[num/2-1]+x[num/2])/2;

cout<<" Median of Even Data is "<<Eloc;

}

return 0;

}

Input

Odd Data

Enter Total Number 9

X

5

7

9

8

3

2

1

6

4

 Given Data is: 5, 7, 9, 8, 3, 2, 1, 6, 4,

 Arange : 1, 2, 3, 4, 5, 6, 7, 8, 9,

 Median of Odd Data is 5

Output

Input

Even Data

Enter Total Number 8

X

5

1

2

9

7

3

2

4

 Given Data is: 5, 1, 2, 9, 7, 3, 2, 4,

 Arange : 1, 2, 2, 3, 4, 5, 7, 9,

 Median of Even Data is 3.5

Output

Median of Group Data Code / Program in C /C++

#include<iostream>

using namespace std;

int main(){

float num,sumf=0,median=0,sumCF=0;

float start[10],end[10],f[10];

cout<<" \t\t <<----- Median Of Grouped Data ----->> "<<endl<<endl<<endl;

cout<<"Enter Total Number ";

cin>>num;

cout<<"Enter Class Intrvals"<<endl;

for(int i=0;i<num;i++){

cout<<i+1<<"- Range Start ";

cin>>start[i];

cout<<i+1<<"- Range End ";

cin>>end[i];

}

for(int i=0;i<num;i++){

cout<<i+1<<"- Enter Frequency of this Range ";

cin>>f[i];

}

int CF[10],loc,index;

float CBStart[10],CBEnd[10];

for(int i=0;i<num;i++){

sumf=sumf+f[i];

CF[i]=sumf;

CBStart[i]=start[i]-0.5;

CBEnd[i]=end[i]+0.5;

loc=sumf/2;

}

for(int i=0;i<num;i++){

if(CF[i]>=loc){

index=i;

i=num;

}

}

cout<<endl;

cout<<"Class Interval Frequency Class Boundaries Cumulative Frequency"<<endl;

for(int i=0;i<num;i++){

cout<<start[i]<<" - "<<end[i]<<"\t\t"<<f[i]<<"\t\t"<<CBStart[i]<<" - "<<CBEnd[i]<<"\t\t\t"<<CF[i]<<endl;

}

float l,h,f1,c;

l=CBStart[index];

h=(end[index]-start[index])+1;

f1=f[index];

c=CF[index-1];

cout<<endl;

cout<<" Lower Class Boundary (l) "<<l<<endl;

cout<<" Hight (h) "<<h<<endl;

cout<<" Frequency oF Location (f) "<<f1<<endl;

cout<<" Sum of Frequency (Sum(f) "<<sumf<<endl;

cout<<" C (C) "<<c<<endl;

cout<<endl;

median=(l+(h/f1)*((sumf/2)-c));

cout<<"Median = l+(f/n)*((sum(F)/2)-c) = "<<median;

return 0;

}

Input

Enter Total Number 5

Enter Class Intrvals

1- Range Start 2

1- Range End 4

2- Range Start 5

2- Range End 7

3- Range Start 8

3- Range End 10

4- Range Start 11

4- Range End 13

5- Range Start 14

5- Range End 16

1- Enter Frequency of this Range 6

2- Enter Frequency of this Range 3

3- Enter Frequency of this Range 9

4- Enter Frequency of this Range 10

5- Enter Frequency of this Range 12

Output