3

Mean Median Mode

Difficulty: EASY
Contributed By
Ankit Kharb
Avg. time to solve
10 min
Success Rate
80%

Problem Statement

You are given an array 'ARR' of 'N' integers and you have to calculate 3 things for the given array:-

1. Mean - function mean(): This function should calculate the mean of the array.

2. Median - function median(): This function should calculate the median of the array.

3. Mode - function mode(): This function should calculate the mode of the array.

Note :
It can be shown that Mean and Median is in the form of P/Q, where P and Q are coprime integers and Q != 0. You need to return P and Q.

For Mode, if the highest frequency of more than one element is the same, return the smallest element.

For Example, for the given array {1, 1, 2, 2, 3, 3, 4}, the mode will be 1 as it is the smallest of all the possible modes i.e 1, 2 and 3.
Input format :
The first line of input contains an integer T denoting the number of queries or test cases. 

The first line of every test case contains an integer N denoting the size of the input array.

The second line of every test case contains N single space-separated integers representing the elements of the input array. 
Output format :
For each test case, 
The first line of output will contain 2 single space-separated integers representing P, and Q for the Mean of the array.

The second line of output will contain 2 single space-separated integers representing P, and Q for the Median of the array.

The third line of the output will contain an integer representing the Mode of the array.
Note :
You do not need to print anything, it has already been taken care of. Just implement the given functions.
Constraints :
1 <= T <= 5
1 <= N <= 10^5 
1 <= ARR[i] <= 10^6 

Where 'ARR[i]' denotes the 'ith' element of the array.

Time limit: 1 sec
Sample input 1 :
1
4  
3 3 1 4 
Sample output 1 :
11 4
3 1
3
Explanation of sample input 1 :
To find the mean, we will take the sum of all the elements and then divide them by the total number of elements. Thus, (3 + 3 + 1 + 4)/4 = 11 / 4. Where P = 11 and Q = 4 and P, Q are coprime. 

To find the median, we will sort the array in ascending order and find the average of n/2 and (n/2 + 1)th number if N is even and (n+1)/2th number if N is odd. Thus, (3+3)/2 = 6 / 2. Thus P = 3 and Q = 1 and P, Q are coprimes.

To find the mode, we will find the element with the highest frequency which is 3 with a frequency of two and thus, the Mode is 3.  
Sample input 2 :
1
5
7 6 5 5 3
Sample output 2 :
26 5 
5 1 
5 
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