Combining Standard Deviations

Hi Everyone,

I am looking to create a formula based on the following MathJax formula but for N = X where X is many numbers rather than just 2 means + SDs. In other words, I want to create an Excel sheet can calculate this automatically for me based on the number of populations (means + SDs) that I enter. I was trying to use sumproduct, count, and sum functios but the brackets became confusing. Essentially, my columns are as per the Excel file attached and the formula I need is also in the excel file. I know my Excel file only goes to 40 rows, but if I added more rows, I was hoping the formula would automatically adjust. The correct formula can be found at the following link under the "Combined Standard deviation:" section which can be viewed after clicking Find on the example values provided at the top: atozmath.com/CONM/Ch2_CombinedSD.aspx. Having an Excel document just makes it easier for further data analysis where I can link cells from different sheets as opposed to manually typing all of my data in online each time and this website could be unavailable too. Another thread from 2015 on here could do this, but again just for two means and SDs rather than an N that can change (excelforum.com/excel-formulas-and-functions/1106578-combine-standard-deviations.html). I attached a sample XLSX document with a screenshot of the formula for two sample means + SDs for your reference. I hope this makes some sense.

Thanks so much!