Need help with Calculating Averages

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Discussion Overview

The discussion revolves around calculating averages, specifically in the context of time spent on classes, subjects, and homework. Participants explore different methods of calculating mean averages from raw data and express confusion over discrepancies in their results.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion over obtaining different results from two methods of calculating averages and questions the correctness and accuracy of each method.
  • Another participant suggests that a weighted average is necessary when averaging between averages, providing a simplified example to illustrate this point.
  • A participant seeks clarification on why their application of the weighted average concept led to different results, indicating a lack of understanding of the underlying principles.
  • Concerns are raised about the influence of busy weeks with more classes on average calculations, suggesting that total hours and classes should be considered for a more accurate average.
  • One participant attempts to apply the weighted average directly but finds discrepancies between their results and those obtained through averaging averages, seeking further explanation.
  • A participant acknowledges the simplicity of the concept but finds it deceptive, indicating a resolution to their confusion while still valuing the input from others.

Areas of Agreement / Disagreement

Participants express differing views on the methods of calculating averages, with some advocating for the use of weighted averages while others question the validity of their results. The discussion remains unresolved regarding the exact reasons for the discrepancies in calculations.

Contextual Notes

Participants mention specific calculations and datasets, but the discussion does not resolve the underlying assumptions or definitions that may affect the results. There is an indication of missing clarity on how to properly apply the concept of weighted averages.

Astro
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Hello,

To anyone who knows a lot about calculating averages:

I NEED HELP WITH:

I need some help with some statistical calculations regarding how much time is spent on classes, subjects, and homework at school. I am trying to calculate the mean average from some raw data and what puzzles me is that when I use two different ways to calculate the answer I get two different results.

I think both of my methods are correct so I'm guessing that the reason for the discrepancy is because I used slightly different ways to derive my answer. However, I can't shake the feeling that the answers should be identical and I don't really understand why they are not.

I WOULD LIKE TO KNOW / NEED HELP WITH:

Which method is correct? Are both methods correct? Is one more accurate then the other, and if so, why? And if one method is wrong, then why?

Please see attached PDF file for all my calculations and the specific problem I'm having.

Thank you in advance for anyone who helps. I'm stumped atm. x3
 

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This is a typical problem where a weighted average is needed if you average between averages.

Let's consider a simplified example. We collect two datasets, raw values:
set A: 4, 8, 7, 8, 5, 4
set B: 76, 80

All values together have an average of 24.
Set A has an average of 6.
Set B has an average of 78.
The average of the averages is (6+78)/2=42, much higher than the average of all values because the two large values had the same "influence" as the 6 small values in this average.
 
Hello and thank you for your answer.

I thought I understood your answer but when I applied it, this happened (see Page 3). Why is this happening?
 

Attachments

Check the average for engineering.
 
One problem is that the busy weeks have more classes than the other weeks. Since your numbers are on a per-class basis, the high and low averages shouldn't count equally. Why don't you just total the hours and the classes and calculate the average hours per class directly?
 
mfb said:
Check the average for engineering.

Oh! x3 I didn't see that; thanks for pointing it out. :3

However, even when I make the correction, the two final calculations still aren't identical and I'm still not sure why.

In the PDF in my previous post, the correct average hours/class for Engineering is=[(1.5x2)+(3x1)]/(2+1)=2 h/class . When I put the corrected value of 2 into the "weighted average of averages sets #1-#5" (see Page 3 of the PDF) , I now get 1.4. 1.4 is still ≠ 1.4117... derived from the other calculation. :-{ Can someone please explain why the answers are not identical? Shouldn't they be identical?
 
Last edited:
FactChecker said:
One problem is that the busy weeks have more classes than the other weeks. Since your numbers are on a per-class basis, the high and low averages shouldn't count equally. Why don't you just total the hours and the classes and calculate the average hours per class directly?

Hello,

In his initial post in this thread, user "Mfb" stated that "a weighted average is needed if you average between averages". I wanted to test that so I decided to first try to solve for the weighted average by calculating the individual averages of hours per class for each subject and then averaging the averages.

When I calculated the weighted average directly as you suggest, the answer I got was different. I'm just trying to understand why the two approaches aren't producing the same answer. As far as I can tell, they should--but clearly I'm still not understanding something.

Note: With regard to the "low averages", I'm ignoring those figures for now. For the sake of simplicity, sets #1 to #5 that I indicated in my PDF of April 16th only only use figures for the busiest possible week. Right now, I'm just trying to test the concept of "a weighted average is needed if you average between averages" .

I still need help though. Can someone please explain why the answers which were calculated slightly differently are not identical? (ie. Why is one answer 1.4 and the other is 1.4117... ?? Shouldn't they be identical? What's wrong with my logic? What am I missing?)
 
I think I solved it!

User Mfb, I like your explanation. :) However, the concept is so simple it's deceptive. x3

See the PDF for my solution (along with the explanation).

Thank you everyone for your help! :3
 

Attachments

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