Standard Deviation of Averages

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Discussion Overview

The discussion revolves around calculating the standard deviation of average bird catches per person based on grouped data. Participants explore the implications of using group averages versus individual data for statistical calculations, particularly focusing on the standard deviation in the context of averages and population data.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents data categorized into 42 groups based on bird catch, seeking to understand how to calculate the standard deviation of averages for these groups.
  • Another participant questions the clarity of the data and the purpose of averaging, suggesting that the average and standard deviation calculations may not align with the provided figures.
  • A later reply clarifies that the goal is to find the average catch per person and whether the standard deviation of the total catch can be divided by the number of people to find an average standard deviation per person.
  • Several participants assert that to accurately calculate the standard deviation per person, individual catch data is necessary, rather than relying on group averages.
  • One participant expresses frustration over repetitive responses that do not contribute new information to the discussion.

Areas of Agreement / Disagreement

Participants generally agree that individual catch data is required for accurate standard deviation calculations. However, there is disagreement regarding the interpretation of the data and the appropriateness of the proposed calculations.

Contextual Notes

There are limitations in the clarity of the data presented, including assumptions about the number of birds caught per person and the implications of averaging group data versus individual data. The mathematical steps involved in calculating standard deviations from grouped versus individual data remain unresolved.

JohnFishy
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Any help would be much appreciated:

My data is grouped into 42 categories according to classification of bird catch. Each group contains "X" amount of species, but for ease of input we categorize them into subsets. For example:

Group 1: 265.5 kg
Group 2: 47 kg
Group 3: 213.5 kg
etc...
Group 42: 63 kg

The sum is equal to 4765 kg. However, to get the average, the total is divided by 400 which is the total amount of birds per people catching them. Hence, the average catch per person is roughly 12 birds. Now if I take the std. deviation of the groups' averages (4765 kg) I get 92.6. Dividing that by 400 I get 0.23 kg.

My question is this; can I simply take the standard deviation of the 'population' whole (each group's average) and divide it by 400? Or is it much more complex due to squaring. Do I need to collate the entire data set into weight of individual birds (not groups)? If I take the std. deviation of every individual birds weight, the result is 3.19 kg. However, this is for every bird not birds/person.

Regards,
 
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Hello John, welcome to PF :smile: !

Not clear to me what the data you show represent. Nor what you want to obtain by taking an average.
What I read: An unspecified number of persons go bird catching. Each person catches on average 400 birds ?
In total 4765 kg of bird is caught (yuch !)

The birds are categorized in groups by species.

Then what does averaging do for you ? Let alone determining the standard deviation ?

I don't believe the numbers either: if the sum is 4765 kg and there are 42 groups then the average is 113 kg per group and the standard deviation will be much less than 93 kg.
 
Im sorry for not clarifing more. There are 400 people, what I wish to obtain is an average catch per person with a standard deviation. So, can I take the standard deviation of the whole (4765 kg) and divide that by 400 to get the average std. deviation of bird weight catch per person?
 
JohnFishy said:
Im sorry for not clarifing more. There are 400 people, what I wish to obtain is an average catch per person with a standard deviation. So, can I take the standard deviation of the whole (4765 kg) and divide that by 400 to get the average std. deviation of bird weight catch per person?
No. If you want that, you will need to have a list of the weight caught by each individual person. That is not a list of the weight caught in the 42 groups.
 
BvU said:
No. If you want that, you will need to have a list of the weight caught by each individual person. That is not a list of the weight caught in the 42 groups.
 
JohnFishy said:
BvU said:
No. If you want that, you will need to have a list of the weight caught by each individual person. That is not a list of the weight caught in the 42 groups.
Not a helpful reply if all you do is quote a previous post.
 

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