$Weighted average issue$

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$Weighted average issue$

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!

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Ericdp326

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Hi Ericdp326,

To identify the weighted number of each data point, you can divide the frequency of each data point by the total frequency. This will give you the weight of each data point. Here's how to do it:

Weighted score for 3.5 = $3.5\times \frac{25}{25+25+20+10+10+10}=0.875$
Weighted score for 4 = $4\times \frac{25}{25+25+20+10+10+10}=1$

And so forth.

The sum of these individual scores add up to 3.525 which is the weighted average of all data points.

You can use these scores (i.e. weights) to calculate the weighted average manually or input them into your CMS to get the correct result.

Best,
Kav10

Extra:

If you want to modify/adjust each data and then the average of those adjusted numbers be 3.525, you can do this:

Calculate the average of the weights. $\frac{25+25+20+10+10+10}{6} =16.66$ . 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

Ericdp326

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
  
  You mean you want to modify/adjust each data and then the average of those adjusted numbers be 3.525?
Ericdp326

Yes, exactly.
Ericdp326

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
  
  Clarification, each of the same weighting as above (e.g., 25%, 25%, 20%, 10%, 10%, 10%)
Kav10

That is easy too.
Kav10

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.
- Ericdp326
  
  Thank you Kav10!!
Kav10

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

$Weighted average issue$

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