Statistics

To simplify and clarify the explanation on updating the standard deviation when a new data point is added, consider the following:Mean Calculation:Original Data Mean:The mean of the original data set is given by: New Data Set Mean:When a new data point is added, maintaining the same mean : Solving for : Standard Deviation Calculation:Original Standard Deviation:The standard deviation of the original data set is: Calculate Variance of the New Data Set:The variance for the new data set is: Breaking it down: Since , . Thus: Equating Variance Values:Since , we have: Substitute in new variance formula: New Standard Deviation:The new standard deviation is: Thus, the standard deviation of the updated data set is .