How to avoid mean of the means I have some data on the presence of plants. My goal is to find the average number of plant species per habitat. The problem is that the number of squares where they have been looking for the plant species varies in numbers - some of the habitats has been looked at in around 200 squares, while others have been looked at in around 50. To make a mean out of the means of each area is wrong, isn't it? /
Example:
Habitat 1, Area 1: 234 species in 200 randomized squares.
Habitat 1, Area 2: 543 species in 57 randomized squares.
Habitat 1, Area 3: 55 species in 22 randomized squares.
Habitat 2, Area 4: 24 species in 83 randomized squares.
Habitat 2, Area 5: 25 species in 84 randomized squares.
Habitat 3, Area 6: 94 species in 20 randomized squares.
Habitat 3, Area 7: 237 species in 36 randomized squares.   
I would really appreciate some help - thank you so much in advance.. 
 A: I believe it depends on how you want to define it. Taking means of the means is not wrong itself if that is what you want to report. Here are a few options:


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*"The average number of plant species per Habitat" as you define it: $\frac{(234+543+55)+(24+25)+(94+237)}{3}$ 


Note that unique plants per habitat might actually be less than the sums in parentheses if there are overlaps of species in areas within an habitat. If you can calculate it, put the unique plants instead for the sums in parentheses above.


*

*The average number of plant species per Area:  $\frac{234+543+55+24+25+94+237}{7}$

*The average density of plant species per Habitat: $\frac{\frac{234+543+55}{200+57+22} + \frac{24+25}{83+84} + \frac{94+237}{20+36}}{3}$

*The average density of plant species per Area: 
$\frac{\frac{234}{200}+\frac{543}{57}+\frac{55}{22}+\frac{24}{83}+\frac{25}{84}+\frac{94}{20}+\frac{237}{36}}{7}$

*The average density of plant species: $\frac{234+543+55+24+25+94+237}{200+57+22+83+84+20+36}$

