There can be a problem with using the arithmetic mean. This is due to community sizes frequently following a [url=https://en.wikipedia.org/wiki/Log-normal]log-normal distribution[/url]. In this case the arithmetic mean will tend to overestimate the central tendency ([url=https://en.wikipedia.org/wiki/Average]average[/url]) because the arithmetic mean can be strongly influenced by a small number of very large communities. The problem of the relevant average to use can also apply to variables such as household size, livestock ownership, income, weight, growth, lengths of stay in a CMAM program. The arithmetic mean is often not an appropriate measure. The effect of this is that you may fail to meet the planned survey sample size. This means that your result will have worse precision than you wanted. You can minimise the problem by using the [url=https://en.wikipedia.org/wiki/Geometric_mean]geometric mean[/url] (the antilogarithm of the means of the logarithms of community populations) or the median of community populations. Another (secondary) issue is that a "law of averages" does not really exist in the sense that a small sample will inevitably even out a random variable. In our context this means that we have no guarantee that the average community size in the sample will be very close to the average community size in the population. Sometimes we will not achieve the planned sample size and sometimes we will exceed the overall sample size. The way to minimise this issue is to increase the number of communities that you sample. This is not a big issue because the number of communities sampled is usually quite a large proportion of the number of communities that could be sampled (i.e. we have a high sampling fraction). I hope this helps.