# Average of averages?

#### niravrph

##### New member
Hi,

How do I calculate the average of some averages? I have the following data:

 # of Meetings # of Attendees total Avg. Attendees per Meeting 84 1011 12.0 84 866 10.3 68 860 12.6

How do I calculate the average of these Averages (third column in table above)?

Thanks!
NIRAV

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi,

How do I calculate the average of some averages? I have the following data:

 # of Meetings # of Attendees total Avg. Attendees per Meeting 84 1011 12.0 84 866 10.3 68 860 12.6

How do I calculate the average of these Averages (third column in table above)?

Thanks!
NIRAV
Depends on what are you using that number for.

One answer would be [(12.0+10.3+12.6)/3 =] 11.7

Another would be [(1011+866+860)/(84+84+68) =] 11.6

Pretty close - but different

#### soroban

##### Elite Member
Hello, niravrph!

How do I calculate the average of some averages? . You don't!

I have the following data:

. . $$\displaystyle \begin{array}{ccc}\text{Meetings} & \text{Attendees} & \text{Average} \\ 84 & 1011 & 12.0 \\ 84 & 866 & 10.3 \\ 68 & 860 & 12.6 \end{array}$$

Subhotosh's second answer is the correct one.

. . $$\displaystyle \begin{array}{cccc} & \text{Meetings} & \text{Attendees} & \text{Average} \\ & 84 & 1011 & 12.0 \\ & 84 & 866 & 10.3 \\ & 68 & 860 & 12.6 \\ \hline \text{Total} & 236 & 2737 \end{array}$$

The average attendance per meeting is: .$$\displaystyle \dfrac{2737}{236} \:=\:11.59745763 \:\approx\:11.6$$

A safe policy is: NEVER average averages.
.

#### Subhotosh Khan

##### Super Moderator
Staff member
I would not say never. It is used all the time in product quality control.

In material testing, where testing are conducted on batches (group of specimens) and lots (groups of batches) and runs (groups of lots) - the statisctic is grouped and and analyzed accordingly.

That is why I used "depends".

#### soroban

##### Elite Member

Suppose we have two machines, A and B.

Machine A produced 90 items and 9 were defective: 10% defective.
Machine B produced 10 items and 5 were defective: 50% defective.

Would you say that on the average the two machines
. . produced: $$\displaystyle \dfrac{10\%+ 50\%}{2} \:=\:30\%$$ defective?

No, out of 100 items only 14 were defective.
. . The average is 14% defective.

There are certain conditions in which averages can be averaged.
. . As I said, it is safer to avoid averaging averages.
.

#### niravrph

##### New member
Thank you, both! I really appreciate it.