# Evaluate Sample Representativeness of Dataset

I'm trying to check / evaluate how representative a sample is from a dataset.

I'm interested in two things:

1. Which sample best represents the original dataset
2. Is the sample a "good enough" representative of the dataset

Example scenario: I have a dataset

original:

> head(mtcars,n=10)
mpg cyl  disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
Duster 360        14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
Merc 240D         24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
Merc 230          22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
Merc 280          19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4


and I take 4 samples, sample1 will have 20% of the records, sample2 will have 40%, sample3 will have 60% and sample4 will have 80% of the original dataset (taken at random).

I want to be able to compare these 4 samples with the original and show how their representativeness changes as the percentage changes, even though, all could be good and bad representatives, the larger samples should have a larger chance of being representative (ie I will run the test multiple times).

I have tried using RMSE, MASE, Chi Sq test and a couple of other methods in R but with no luck.

Any and all help will be greatly appreciated!