Array Average

#include <iostream>
#include <iomanip>
using namespace std;

int main() {
    int n;
    double sum = 0;
    
    cout << "Enter number of elements: ";
    cin >> n;
    
    int arr[n];
    
    cout << "Enter " << n << " elements: ";
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
        sum += arr[i];
    }
    
    double average = sum / n;
    
    cout << fixed << setprecision(2);
    cout << "Average of array elements: " << average << endl;
    
    return 0;
}

Enter number of elements: 5
Enter 5 elements: 10 20 30 40 50
Average of array elements: 30.00

This program teaches you how to calculate the average of all elements in an array in C++. The average (also called the mean) is calculated by summing all elements and dividing by the total number of elements. This is a fundamental array operation that demonstrates how to iterate through arrays, accumulate values, and perform calculations with arrays.

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1. What is an Array Average?

The average of an array is the sum of all elements divided by the number of elements.

Formula:

Average = (Element1 + Element2 + ... + ElementN) / N

Example:

If array = [10, 20, 30, 40, 50]

• Sum = 10 + 20 + 30 + 40 + 50 = 150
• Number of elements = 5
• Average = 150 / 5 = 30.00

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2. Header Files

The program uses two header files:

1. #include <iostream>

   • Provides cout for output and cin for input

2. #include <iomanip>

   • Provides fixed and setprecision() for formatting decimal output
   • Ensures the average is displayed with exactly 2 decimal places

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3. Variable Declarations

cpp
int n;
double sum = 0;
int arr[n];
double average;

Explanation:

• n: Stores the number of elements in the array (integer)

• sum: Accumulates the sum of all array elements (initialized to 0)

  • Uses double to handle decimal results accurately

• arr[n]: The array to store the elements

  • Size is determined by user input n

• average: Stores the calculated average (double for decimal precision)

Why double for sum and average?

• Even if array elements are integers, the average might be a decimal
• Example: Average of [1, 2, 3] = 2.00 (decimal result)
• Using double ensures accurate decimal calculations

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4. Taking Input: Number of Elements

cout << "Enter number of elements: "; cin >> n;

The program first asks the user how many elements they want to enter. This determines the size of the array.

Example: If user enters 5, then n = 5, and the array will have 5 elements.

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5. Declaring the Array

int arr[n];

This creates an array of size n to store the elements.

Note: Variable-length arrays (VLAs) like this work in some C++ compilers, but the standard approach is to use vectors or dynamic allocation. However, for beginners, this syntax is simpler to understand.

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6. Taking Input: Array Elements

cpp
cout << "Enter " << n << " elements: ";
for (int i = 0; i < n; i++) {
    cin >> arr[i];
    sum += arr[i];
}

Step-by-step:

1. The program asks the user to enter n elements
2. A loop runs from i = 0 to i < n (0-indexed)
3. For each iteration:
   • cin >> arr[i]; reads one element and stores it in the array
   • sum += arr[i]; adds the element to the running sum

Example with n = 5:

• User enters: 10 20 30 40 50
• Iteration 1: arr[0] = 10, sum = 0 + 10 = 10
• Iteration 2: arr[1] = 20, sum = 10 + 20 = 30
• Iteration 3: arr[2] = 30, sum = 30 + 30 = 60
• Iteration 4: arr[3] = 40, sum = 60 + 40 = 100
• Iteration 5: arr[4] = 50, sum = 100 + 50 = 150

Key Technique: Accumulation

• sum += arr[i]; is equivalent to sum = sum + arr[i];
• This accumulates (adds up) all values as we read them
• By the end of the loop, sum contains the total of all elements

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7. Calculating the Average

double average = sum / n;

This line calculates the average by dividing the sum by the number of elements.

Important: Since both sum and average are double, the division will be floating-point division, giving a decimal result.

Example:

• sum = 150 (as double: 150.0)
• n = 5
• average = 150.0 / 5 = 30.0

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8. Formatting the Output

cpp
cout << fixed << setprecision(2);
cout << "Average of array elements: " << average << endl;

fixed:

• Ensures numbers are displayed in fixed-point notation (not scientific notation)
• Example: 30.00 instead of 3e+01

setprecision(2):

• Sets the number of decimal places to 2
• Example: 30.0 becomes 30.00, 25.5 stays 25.50

Why format the output?

• Makes the result look professional and consistent
• Important for financial, scientific, and statistical applications
• Users expect a certain number of decimal places

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9. Complete Program Flow

1. Ask user for number of elements (n)
2. Declare array of size n
3. Initialize sum = 0
4. Loop through array:
   • Read each element
   • Add to sum
5. Calculate average = sum / n
6. Format output to 2 decimal places
7. Display the average

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10. Key Concepts Demonstrated

1. Array Input: Reading multiple values into an array using a loop

2. Accumulation Pattern: Using sum += arr[i] to accumulate values is a common pattern in programming

3. Type Conversion: Using double ensures decimal division even when dividing integers

4. Output Formatting: Using fixed and setprecision() for professional-looking output

5. Array Traversal: Iterating through all elements of an array using a for loop

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11. Common Variations

Variation 1: Calculate average separately (two loops)

cpp
// First loop: Read elements
for (int i = 0; i < n; i++) {
    cin >> arr[i];
}
// Second loop: Calculate sum
for (int i = 0; i < n; i++) {
    sum += arr[i];
}

Variation 2: Using float instead of double

cpp
float sum = 0, average;
// ... rest of code

Variation 3: Finding average of specific range

cpp
// Average of first 3 elements only
for (int i = 0; i < 3; i++) {
    sum += arr[i];
}
average = sum / 3;

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12. Common Mistakes

1. Not initializing sum: Forgetting sum = 0 gives incorrect results

2. Integer division: Using int for sum/average loses decimal precision

3. Wrong loop bounds: Using i <= n instead of i < n (array out of bounds)

4. Dividing by zero: If n = 0, division by zero causes error

5. Not formatting output: Missing fixed << setprecision(2) gives inconsistent decimal places

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13. Practical Applications

Array averages are used in:

• Statistics: Calculating mean values

• Data Analysis: Analyzing datasets

• Grading Systems: Calculating student averages

• Performance Metrics: Average scores, times, etc.

• Financial Calculations: Average prices, returns, etc.

• Scientific Computing: Average measurements, readings

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14. Edge Cases to Consider

1. Empty array: n = 0 → Division by zero error

2. Negative numbers: Works fine, but average might be negative

3. Very large numbers: May cause overflow if using int for sum

4. Very small numbers: Precision issues with floating-point

Improved version with error checking:

cpp
if (n <= 0) {
    cout << "Error: Number of elements must be positive!" << endl;
    return 1;
}

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Summary

• The program reads n elements into an array.
• It accumulates the sum of all elements using sum += arr[i] in a loop.
• The average is calculated as sum / n.
• double is used for sum and average to ensure decimal precision.
• Output is formatted to 2 decimal places using fixed << setprecision(2).
• This creates a clean, professional program for calculating array averages.

This program is essential for understanding array operations, accumulation patterns, and output formatting. It's a fundamental building block for more complex array manipulations and statistical calculations.