Testing whether the variance of a data set is significant hope someone can help me out with some stats for a data set I have- I originally thought it was easy but I think I'm over complicating everything in my head.
Ok so for example- I'm looking at the body length of dogs. I've taken measurements of 20 individuals of each breed and I've done this for 10 breeds. I now want to see if the measurements I've taken for each breed are a good representative of the actual breed- so I think I want to see if the variance for each breed is significant and then decide overall if all these variances are significant so that I can tell when I compare the breeds if I've actually got means that are representing the breed.
Plotted coefficient of variation against the breeds mean as suggested: 

Still confused about how (or if its possible) I can tell if the variance within the breeds is significant. Would performing a stats test on the coefficients of Variance work?
 A: 
I now want to see if the measurements I've taken for each breed are a
  good representative of the actual breed

This is impossible based on the sample itself. I understand what you want but it can't be done without knowing something in addition to the sample at hand, something about the entire population (i.e. breed in this case).
For instance, you know what is the average weight of dogs in the population ( for entire breed), then you look at your 10 dogs and their weight is somehow not representative, then you have an issue with the sample. You probably can't use the length measurements either.
Another example, suppose you know that the variance of length in population is $\sigma^2=100$. You measure the variance in 10 dog sample and it's $S^2=1000$. If we assume that the variance of sample variance $S^2$ is $\sigma^4/n=100^2/10=1000$, then the standard deviation is approximately $\sqrt{1000}\approx 33$, hence $S^2=1000$ is too high relative to $\sigma^2=100$. Note, we established that the sample variance was too high using external information, in this case the population variance
