I have a range of readings from a test (for example:0.796, 0.109, 0.11, 0.11, 0.109, 0.109, 0.109, 1.78). I want to remove the extraneous values of these so that I get a more realistic view on the more accurate test result range. If I take the average (1.78) or the median (1.09) it doesn't give me that picture. I am not able to figure out how I could mathematically have a way to achieve this, because I don't want these extraneous values to skew my results.
I get the impression you're talking about excluding outliers.
Exactly what should count as one (and whether they should be removed at all) sort of depends on your own views (like what 'accurate test result range' means) and your purposes.
It sounds like you might actually just need a reasonably robust estimate of scale; there are many such.
i) the quartiles for your data (using the default definitions in R) are 0.1090 and 0.2815; the interquartile range for your data is then 0.1725. The middle 50% of the data lie in between 0.1090 and 0.2815.
ii) the median absolute deviation from the median (MAD) is 0.0005; 50% of the data lie between median-MAD and median+MAD.