Program3(a)

3.a. Read N numbers from the console and create a list. Develop a program to print mean, variance and standard deviation with suitable messages.

Objective of the Program

• To understand list creation from user input

• To perform statistical calculations

• To use loops for computation

• To apply mathematical formulas in programming

Logical Construction (Think Before You Code)

Before writing the program, understand the mathematical formulas clearly.

Suppose the list contains N numbers:

x1, x2, x3, ... , xN

1.Mean (Average)

                                            Mean=(Sumofallelements)/N

2.Variance

$$Variance=\frac{\sum (xi-Mean{)}^2}{N}$$

Steps:

• Subtract mean from each element

• Square the result

• Add all squared values

• Divide by N

3.Standard Deviation

                                                         Standard Deviation=SQRT(Variance)​

Program Logic Steps

1. Read N

2. Create empty list

3. Read N numbers and store in list

4. Compute sum

5. Calculate mean

6. Compute squared differences

7. Calculate variance

8. Calculate standard deviation

9. Display results

👉 The key idea:
First compute mean, then use it to compute variance, then compute standard deviation.

Flowchart (Block Diagram of Logic)

Flowchart Explanation

• Start

• Read N

• Input N numbers into list

• Calculate sum

• Compute mean

• Compute variance

• Compute standard deviation

• Display results

• Stop

Algorithm

1. Start

2. Read N

3. Initialize empty list

4. For i from 1 to N

   • Read number

   • Append to list

5. Calculate sum of list

6. Compute mean = sum / N

7. Initialize variance_sum = 0

8. For each element in list

   • variance_sum += (element − mean)²

9. variance = variance_sum / N

10. standard_deviation = √variance

11. Display mean, variance, standard deviation

12. Stop

Python Program

⚠ Students must complete the missing parts.

# Program to calculate Mean, Variance and Standard Deviation

import math

n = int(input("Enter number of elements: "))

numbers = []

for i in range(n):

    value = float(input("Enter number: "))

    numbers.append(__________)

total = sum(__________)

mean = total / __________

variance_sum = 0

for num in numbers:

    variance_sum += (num - __________) ** 2

variance = variance_sum / __________

std_deviation = math.sqrt(____________)

print("Mean =", mean)

print("Variance =", variance)

print("Standard Deviation =", std_deviation)

Probable Output

Case 1

Enter number of elements: 5

Enter number: 2

Enter number: 4

Enter number: 6

Enter number: 8

Enter number: 10

Mean = 6.0

Variance = 8.0

Standard Deviation = 2.8284271247461903

Important Concepts Used

• Lists

• sum() function

• Looping (for)

• Arithmetic operations

• math.sqrt()

• Statistical formulas

Viva Voce Questions

1. What is mean?

2. What is variance?

3. Why do we square the difference?

4. Why is standard deviation square root of variance?

5. Can variance be negative?

6. What happens if N = 0?

7. What is the time complexity of this program?

Procedure to Execute the Program

1. Open Python IDLE / VS Code / Google Colab

2. Create a new file

3. Type the program

4. Save with .py extension

5. Run the program

6. Enter N and the numbers

Google Colab – Online Execution

👉 Paste your Colab link here.

[https://colab.research.google.com/drive/1cUDbj_f5HZbs5k4mlgX5YLK3ONXcub2A?usp=sharing]

Program Explanation

Assignment for Students

• Modify program to calculate sample variance

• Use statistics module instead of manual calculation

• Store results in a dictionary

• Display results rounded to 2 decimal places

Lab Record Instructions

Right Side of the Record
1. Problem Statement
2. Python Program
Write the following neatly on the right-hand side page:

Left Side of the Record
Write the following neatly on the left-hand side page:
3. Flowchart
4. Algorithm
5. Output
⚠️ Students must write ALL possible outputs.

-:END:-