Develop a C program that will perform the following operations on an array containing grades by using appropriate functions. Hard code the array elements (as shown in the output) in the main program and call the respective functions. The main function should print the array values before the array change and array values after the array change. Do not use global variables. The three different functions respectively should a) calculate the standard deviation and return the standard deviation. b) add the standard deviation (use the integer portion after rounding up) to each of the original array elements. If the new value exceeds 100, the final value should be limited to 100. c) Sort the array using modified bubble sort. The bubble sort presented in Fig 6.15 of the text is inefficient. Instead of making the same number of comparisons for every pass, modify it so that for every successive pass, it makes one less comparison from the previous pass. d) To verify the correctness of the modified sorting approach, try using different combinations of numbers (different test cases). e) The functions should be able to work with any array size, where applicable. The expected output of the program Exam scores: 90 95 90 82 80 87 92 Standard deviation: 4.9857 Adjusted exam scores: 95 100 95 87 85 92 97 Sorted exam scores: 85 87 92 95 95 97 100

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**Develop a C Program to Manipulate Grades in an Array**

This educational resource outlines the steps to develop a C program that performs specific operations on an array containing grades. The operations are executed through functions that handle calculations and modify the contents of the array. It is important to note that global variables should not be used in the development of the program.

### Operations and Function Requirements

1. **Standard Deviation Calculation**
   - Create a function to calculate and return the standard deviation of the grades.

2. **Adjust Grades**
   - Develop a function to add the standard deviation (rounded up) to each grade.
   - If a new grade exceeds 100, limit it to 100.

3. **Sort Grades with Modified Bubble Sort**
   - Implement a sorting function using a modified version of bubble sort.
   - For each pass, reduce the number of comparisons by one to improve efficiency.

4. **Verification**
   - Test the modified sorting method with various datasets to ensure correctness.

5. **Function Flexibility**
   - Ensure functions can handle arrays of any size.

### Example Output

The program processes an array of grades and demonstrates its functionality with an example output:

- **Exam Scores:** 90, 95, 90, 82, 80, 87, 92
- **Standard Deviation:** 4.9857
- **Adjusted Exam Scores:** 95, 100, 95, 87, 85, 92, 97
- **Sorted Exam Scores:** 85, 87, 92, 95, 95, 97, 100

Ensure that your program outputs match these results to verify successful implementation.
Transcribed Image Text:**Develop a C Program to Manipulate Grades in an Array** This educational resource outlines the steps to develop a C program that performs specific operations on an array containing grades. The operations are executed through functions that handle calculations and modify the contents of the array. It is important to note that global variables should not be used in the development of the program. ### Operations and Function Requirements 1. **Standard Deviation Calculation** - Create a function to calculate and return the standard deviation of the grades. 2. **Adjust Grades** - Develop a function to add the standard deviation (rounded up) to each grade. - If a new grade exceeds 100, limit it to 100. 3. **Sort Grades with Modified Bubble Sort** - Implement a sorting function using a modified version of bubble sort. - For each pass, reduce the number of comparisons by one to improve efficiency. 4. **Verification** - Test the modified sorting method with various datasets to ensure correctness. 5. **Function Flexibility** - Ensure functions can handle arrays of any size. ### Example Output The program processes an array of grades and demonstrates its functionality with an example output: - **Exam Scores:** 90, 95, 90, 82, 80, 87, 92 - **Standard Deviation:** 4.9857 - **Adjusted Exam Scores:** 95, 100, 95, 87, 85, 92, 97 - **Sorted Exam Scores:** 85, 87, 92, 95, 95, 97, 100 Ensure that your program outputs match these results to verify successful implementation.
**Standard Deviation Calculation Guide**

To accurately calculate the standard deviation of a dataset, follow the steps outlined below. This guide is designed for educational purposes to help you grasp the concept of standard deviation and its calculation in statistical analysis.

### Instructions:

1. **Data Type and Formatting:**
   - Use the `float` data type for numerical calculations.
   - When printing the values of the array, use `printf("%.0f")` to round up the numbers appropriately.

2. **Formula for Standard Deviation:**

   The standard deviation (\(\sigma\)) is calculated using the formula:

   \[
   \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}
   \]

   Here:
   - \(N\) is the total number of data points.
   - \(x_i\) represents each individual data point.
   - \(\mu\) is the mean (average) of the data points.
   - \(\sum\) denotes summation across all data points.

3. **Note:**
   - It might be easier to break down this complex formula into smaller components. By dividing it into manageable parts, you can systematically calculate the standard deviation. First, find the mean (\(\mu\)), calculate the differences from the mean, square those differences, find the average of these squares, and then take the square root of that average.

This approach ensures clarity and accuracy in your calculations while giving you a deeper understanding of statistical methods.
Transcribed Image Text:**Standard Deviation Calculation Guide** To accurately calculate the standard deviation of a dataset, follow the steps outlined below. This guide is designed for educational purposes to help you grasp the concept of standard deviation and its calculation in statistical analysis. ### Instructions: 1. **Data Type and Formatting:** - Use the `float` data type for numerical calculations. - When printing the values of the array, use `printf("%.0f")` to round up the numbers appropriately. 2. **Formula for Standard Deviation:** The standard deviation (\(\sigma\)) is calculated using the formula: \[ \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2} \] Here: - \(N\) is the total number of data points. - \(x_i\) represents each individual data point. - \(\mu\) is the mean (average) of the data points. - \(\sum\) denotes summation across all data points. 3. **Note:** - It might be easier to break down this complex formula into smaller components. By dividing it into manageable parts, you can systematically calculate the standard deviation. First, find the mean (\(\mu\)), calculate the differences from the mean, square those differences, find the average of these squares, and then take the square root of that average. This approach ensures clarity and accuracy in your calculations while giving you a deeper understanding of statistical methods.
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