Standard Deviation Calculation

This program calculates the standard deviation of a set of numbers, which measures the amount of variation or dispersion in the data set. To begin, the program prompts the user to enter the number of data points followed by the data itself. It then computes the mean (average) of the numbers. Using the mean, the program calculates the variance, which is the average of the squared differences between each data point and the mean. Finally, the standard deviation is determined by taking the square root of the variance. This process provides a clear indication of how spread out the data values are around the mean.

Code Breakdown

Algorithm

1. Start

2. Input the Number of Data Points:

   • Prompt the user to enter the number of data points n.

3. Input the Data Points:

   • Initialize an array to store n numbers.
   • Prompt the user to enter each number and store it in the array.

4. Calculate the Mean:

   • Initialize a variable sum to 0.
   • Iterate over each number in the array, adding each number to sum.
   • Compute the mean by dividing sum by n.

5. Calculate the Variance:

   • Initialize a variable sum_of_squares to 0.
   • Iterate over each number in the array:
     • Compute the difference between the number and the mean.
     • Square this difference and add it to sum_of_squares.
   • Compute the variance by dividing sum_of_squares by n.

6. Calculate the Standard Deviation:

   • Compute the standard deviation by taking the square root of the variance.

7. Output the Standard Deviation:

   • Print the standard deviation.

8. End

Code Explanation

Example Flowchart

                            Start
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              Input the number of data points (n)
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               Input n numbers into array x[]
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               Calculate the sum of all numbers
                        in array x[]
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                      Calculate the mean
                       (mean = sum / n)
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                      Initialize sum = 0
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              For each number x[i] in array x[]
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                   Compute (x[i] - mean)²
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                     Add result to sum
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                        End For loop
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                Calculate standard deviation
                    (sd = sqrt(sum / n))
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              Print the standard deviation (sd)
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                             End