Weighted average issue

I have a weighted average question that I'm can't seem to calculate. Here's the calculation:

(25×3.5+25×4+20×2.5+10×4.5+10×3+10×4) / (25+25+20+10+10+10) = 3.525

How do I identify the weighted number of EACH data set from that equation (e.g., 3.5, 4, 2.5, etc.)?

I'm uploading these scores into my company's CMS, but it doesn't have the capability to calculate the weighted average. Without it, those data points will equal 3.58, not 3.525. So, I need to manually input each data point so that the final score comes to 3.525.

Thanks in advance!

Statistics
Ericdp326 Ericdp326
8
Report

Answer

Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
Kav10 Kav10
1.7K
  • Ericdp326 Ericdp326
    0

    Hi Kav10! Thank you for your help with this. I was able to find the summation properly, using your formula above. But the real problem I'm facing is how to make the average of those weighted data points 3.525, not the sum. So, for instance, 3.5 should be remarkably close (say, 3.56), but likely not 3.5 exactly. Does that make sense? Thanks again! Eric

    • Kav10 Kav10
      0

      You mean you want to modify/adjust each data and then the average of those adjusted numbers be 3.525?

  • Ericdp326 Ericdp326
    0

    Yes, exactly.

  • Ericdp326 Ericdp326
    0

    I'm hoping there's a formula I can run to make that happen — I have 10 data sets to calculate (each with the same weighting, but different data points).

    • Ericdp326 Ericdp326
      0

      Clarification, each of the same weighting as above (e.g., 25%, 25%, 20%, 10%, 10%, 10%)

  • Kav10 Kav10
    0

    That is easy too.

  • Kav10 Kav10
    0

    I'll explain it here. Calculate the average of the weights. (25+25+20+10+10+10)/6 = 16.66. Calculate a score for each data point by dividing its weight (i.e. frequency) by the average frequency calculated above (i.e. 16.66). This will give you the adjusted score for each data point. For example, for the first data point (i.e. 3.5), this would be 5.25. And you calculate like that for the other data points. Now, average the new adjusted scores, and the average will be 3.525.

  • Kav10 Kav10
    0

    Of course! Glad I was helpful. Thanks for the coffee.

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.