Comparing the age distribution of two groups with different sample sizes I have a dataset regarding a hotel. I am trying to compare the age distribution of two groups: Leisure and business. The sample sizes of these groups are not equal. The business group has 12.4k entries, and the leisure group has 19.6k entries. In reality, the business group is a lot bigger.
For 18 year olds, the leisure has an absolute value of 66, and the business has a value of 8.
If I want to compare these two, would it be statistically correct to calculate them to percentages (of their own respective groups, i.e. 8/12400 and 66/19600) and compare them then? 
 A: If you want to make no assumption about the distribution of age, consider the two-sample Kolmogorov–Smirnov test. The two-sample Kolmogorov–Smirnov compares the difference in empirical distribution functions (ECDF) of two samples (meaning it considers both location and shape of the the two samples). There are several packages in R for this, one of which is dgof.
If you can assume age is Normally distributed, you can just perform a two sample t-test. If it looks like your data is Normally distributed, you should run a two-sample t-test as this will have the most statistical power. If you want to check how Normal your age data are, you can use the Shapiro-Wilk test (or even just plot the density of age by using plot(density(age)) where age is the vector with the age data in R). 
If you want to just visually compare the densities, let's say you data is in this format:
Age    Group
18     Leisure
27     Business
33     Business
21     Leisure

You can run,
library(ggplot2)
ggplot(data = dat) + geom_density(aes(x = Age, group = Group))

A: I suspect that statistical tests won't be helpful. With such large sample sizes, of course the null hypothesis of exactly equal age distributions will be rejected. 
My suggestion: Draw a graph (histogram) of age distributions in the two groups, and make your conclusions based on looking at the graph, without any statistical testing. 
