Averaging of averages

[robertrao]

Hi,

Can someone explain to the equation why we should not do the average of averages over the entire sample

With an Equation

Thanks

[PaigeMiller]

why we should not do the average of averages over the entire sample

This is a very vague question, as we don't know what your sample looks like and what drawbacks you believe exist for "average of averages".

I'll make a guess, pending further information from you. Average of averages works if every group in the sample has the same sample size; if the sample sizes differ, you may or may not want to use average of averages, depending on what it is you want to estimate.

[robertrao]

2011        MEAN
categoryA     5
categoryB     12
categoryC     14
categoryD     5
categoryE      6
categoryF      7
categoryG      35
categoryH      29
categoryI      27
categoryJ      24
categoryK      15
categoryL      15
categoryM      13
categoryN      39
categoryO      35
categoryP      09
categoryQ      15
categoryR      8
categoryS     9
categoryT     12
categoryU       4
------------------------------
MEAN OF MEAN    16
-----------------------------

VS

2011 MEAN OF ALL VALUES ACROSS CATEGORY A to CATEGORY U=  24

This is by summing all thwe values and doing a normal average of 2011 values instead of averaging of the averages

Regards

[PaigeMiller]

Hi, Robertao

Perhaps you could enlighten us about exactly what it is you are trying to estimate, and what the categories represent, and how the sample was obtained, and what the sample sizes are in each category ... you know, the details that would be important for any statistical analysis.

Because without that, we really can't give you guidance about what to do, or which one to use, all we can say is that obviously the sample sizes are causing the difference, but which one is the right one to use ... can't say without more information.

[ballardw]

Do the categories even make sense to combine? If the average of Category A refers to the number of children in classrooms and Category B refers to number of desks in the classrooms what would the average of those two numbers tell you?

[Reeza]

Its because all categories would be considered equal when they're not.

EG Category A has 5 people but Category B has 10000.

You can get around this by doing a weighted average or by doing a full average as you've indicated.