I have to summarize survey data for smaller samples(n<100). In order to find the correct measure of central tendency for summarizing(mean/median), currently I see the histogram distribution for the data. I want to do this selection between mean and median mathematically rather than visually. Is there a cutoff for variance/ any other statistical measure, which I can roughly use to decide whether to choose mean or median for summarizing?
You could use formal tests for normality. Shapiro–Wilk test being preferred.
But the simplest is to use the skew measure. If abs(skewness(x))<0.8 then according to Dr. Parzen from Harvard University, the data is essentially normal shaped and it is safe to use the mean.
Something to consider, outliers have strong leverage on the mean. Winsorization (clipping) may condition the mean enough for you. What Winsorization does is replace values beneath 0.5 percentile with the 0.5 percentile value and likewise anything above for 99.5 percentile.