# Standard Deviation of Averages

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,

BvU
Homework Helper
2019 Award
Hello John, welcome to PF !

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?

BvU
Homework Helper
2019 Award
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.

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.

Mark44
Mentor
JohnFishy 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.