# How to check if the sample represents the population data?

The below table is similar to the population

      name            designation                      group     division   pay-scale
0   Elizabeth Kent    senior associate - technical       B         CB       [24000, 45000)
1   Thomas Lewis      project lead                       D         EB       [24000, 45000)
2   Joshua Salinas    hardware technician                B         BB       [45000, 60000)
3   Yesenia Johnson   system security engineer           C         BB       [24000, 45000)
4   Becky Washington  system security engineer           C         CB       [60000, 85000)


Now, I have drawn a sample using Proportionate stratified random sampling technique.

     name               designation           group   division  pay-scale
Erik Meza       IT Project Manager            A   AB          [24000, 45000)
Mark Scott      project lead                  A   AB          [45000, 60000)
Jennifer Smith  IT Project Manager            A   BB          [60000, 85000)
Scott Long      hardware technician           A   CB          [24000, 45000)
Phillip Smith   project lead                  A   CB          [60000, 85000)


This is a table which shows how much each group contribute to the population and sample respectively. I am not able to copy paste this table therefore I am adding a picture sorry for the inconvenience.

I would like to know what metrics I could use to check if the sample represents the population for such a sample. Any resurces will be useful. Thankyou!

• Can you just check some summary statistics? For example, Is the proportion of group A in the sample similar to the population? Likewise for the other groups & columns. Commented Apr 6, 2022 at 8:19
• @jcken yes I checked for the individual and group proportions but still need some more statistics into it for proving it Commented Apr 6, 2022 at 9:24
• I'm not really sure what else you can do. May I ask, why do you want to see if your sample represents the population if you already have the whole population? Commented Apr 6, 2022 at 9:31
• Since the survey can't be done on whole population I need a sample which represents the popoulation so good metrics to prove the similarities Commented Apr 6, 2022 at 9:42
• Represemative samples are highly elusive in practice. Suppose there is just one person in the population with one unusual combination of characteristics. Then to be representative every sample must include that person with the appropriate probability of the reciprocal of the population size. You're left with the paradox that the only truly representative sample is a replica of the population. Kruskal and Mosteller dissected the concept at enormous length in a series of articles in 1979 and 1980. Naturally if you fall back on an idea of approximation you then need to spell out what that means. Commented Apr 7, 2022 at 8:13