Question

Write a program that uses the rand function to generate 500 integers, in the range [0,15).

Then calculate the mean and standard deviation.

Answer 1

Solution:

To generate the random number between (0,15) in python

  

import random #Import the random library to generate the random numbers

#Random Generator Function to get the random numbers between the range
def randomNumber_Generator():
 #declare array to store the random numbers    
 randomNumber=[]
 #using for loop generate 500 random numbers between 1to 15
 for i in range(1,500):
  val=random.randrange(0,15); #Using randrange module of random generate number
  randomNumber.append(val) #append value to the list
 return randomNumber; #return list of 500 random numbers
 

Calculate Mean:

Formula to calucale the Mean is S

Sumofthenumber/ sizeofthenumber

for eg let us take list number {1,2,3,4,5} & list size is 5

1+2+3+4+5/5=15/5

15/5=3

mean=5

In our case the Mean formula will be Sum of the each element in random Array/500

Program:

#Method to Calculate MEan value
def CalculateMean(value):
 # Initialize sum as Zero    
 sum=0;
 #Using for loop iterate random array and find sum of all values
 for j in range(0,len(value)):
    sum=sum+value[j];
 #Divide the sum by the length of array
 result=sum/len(value);
 #return result
 return result;

Standart Deviation:

Formula To Calculate StandardDeviation =

n x - n-1 mean) i=1

step 1: Calculate Mean value for the list .Let us Consider above example 1+2+3+4+5=15/5=3

step2: Calculate square of Differente between elements and mean

• 1-3=(-2)^2= 4
• 2-3=(-1)^2=1
• 3-3=(0)^2=0
• 4-3=(1)^2=1
• 5-3=(2)^2=4

step 3: Calculate sum of the square calculated in above steps

4+1+0+1+4=10

step 4 Calculate sumof the square divided by n-1

10/4=2.5

step5: Take Square root of the value = 1.58

V2.5

Similar Steps are followed in the program for the 500 random number

#method to calculatestandarddeviate
def CalculateStandardDeviation(randomNum,m):
 sum=0;
 # loop to calculate sum of (number-mean)^2
 for k in range(0,len(randomNum)):
    sum=sum+(randomNum[k]-m)*(randomNum[k]-m);
 #Divide sum of square by len of array -1 (here it is499)
 result=sum/(len(randomNum)-1);
#return take square root of result and return it
 return math.sqrt(result);

Whole Program:

import math #Import to call sqrt of maths function
import random #Import the random library to generate the random numbers

#Main Method
def main():
 #call the randomNumber_Generator method
 randomNumbers=randomNumber_Generator();
 #Call CalculateMeanMethod to get Mean
 mean=CalculateMean(randomNumbers)
 print("Mean Value:",mean);
 #Call CalculateStandardDeviation to standardDeviation
 standardDeviation=CalculateStandardDeviation(randomNumbers,mean);
 print("Standard Deviation:",standardDeviation); 
 
 #Random Generator Function to get the random numbers between the range
def randomNumber_Generator():
 #declare array to store the random numbers    
 randomNumber=[]
 #using for loop generate 500 random numbers between 1to 15
 for i in range(1,500):
  val=random.randrange(0,15); #Using randrange module of random generate number
  randomNumber.append(val) #append value to the list
 return randomNumber; #return list of 500 random numbers
 
#Method to Calculate MEan value
def CalculateMean(value):
 # Initialize sum as Zero    
 sum=0;
 #Using for loop iterate random array and find sum of all values
 for j in range(0,len(value)):
    sum=sum+value[j];
 #Divide the sum by the length of array
 result=sum/len(value);
 #return result
 return result;
 
 #Method to calculate standardDeviation
def CalculateStandardDeviation(randomNum,m):
 sum=0;
 #Loop to claculate sum of the random number -mean square
 for k in range(0,len(randomNum)):
    sum=sum+(randomNum[k]-m)*(randomNum[k]-m);
#Divide sum by the length of array -1 
 result=sum/(len(randomNum)-1);
 #return square root of the result
 return math.sqrt(result);
 
#Used to call Main Method

if __name__ == "__main__":
    main()

Ouput 1:

Mean Value: 6.8997995991983965

Standard Deviation: 4.414058860324523

Output 2:

Mean Value: 7.110220440881764

Standard Deviation: 4.318387387674145

Output 3:

Mean Value: 6.8937875751503

Standard Deviation: 4.372093582270911

Note:In the above program I didn't used the statistic library to calculate mean and standart deviation.If you want you can import statictics to calculate meann & SD.Kindly refer below code for that

import statistics #Import to call Mean and Standard deviation
import random #Import the random library to generate the random numbers

#Main Method
def main():
 #call the randomNumber_Generator method
 randomNumbers=randomNumber_Generator();
 #Call CalculateMeanMethod to get Mean
 mean=CalculateMean(randomNumbers)
 print("Mean Value:",mean);
 #Call CalculateStandardDeviation to standardDeviation
 standardDeviation=CalculateStandardDeviation(randomNumbers,mean);
 print("Standard Deviation:",standardDeviation); 
 
 #Random Generator Function to get the random numbers between the range
def randomNumber_Generator():
 #declare array to store the random numbers    
 randomNumber=[]
 #using for loop generate 500 random numbers between 1to 15
 for i in range(1,500):
  val=random.randrange(0,15); #Using randrange module of random generate number
  randomNumber.append(val) #append value to the list
 return randomNumber; #return list of 500 random numbers
 
#Method to Calculate MEan value
def CalculateMean(value):
 #Calculate the value using statistics mean method
 result=statistics.mean(value);
 #return result
 return result;
 
 #Method to calculate standardDeviation
def CalculateStandardDeviation(randomNum,m):
#Calculate it by passing array & mean value    
 result=statistics.stdev(randomNum, xbar = m);
 #return square root of the result
 return result;
 
#Used to call Main Method

if __name__ == "__main__":
    main()

Output:

Mean Value: 7.038076152304609

Standard Deviation: 4.387888715055942

Output:

Mean Value: 6.907815631262525

Standard Deviation: 4.224084587277824