How can I take a subsample having almost the same mean and standard deviation of the population?

Question

If this is my data frame:

> length <- rep(11:17, 200)
> mean(length)
[1] 14
> sd(length)
[1] 2.001

How can I take a random subsample from the data frame (length) but having almost the same mean and standard deviation?

Answer 1

You can repeatedly draw from length until you find enough samples that fit your requirements. It is not pretty, but it works.

length <- rep(11:17, 200)

# save mean and sd the subsamples should have
aimed_mean <- mean(length)
aimed_sd <- sd(length)

# set number of replications / iterations
n_replication <- 1000

# set size of sample
size_sample <- 40

# set desired number of samples
n_sample <- 3

# set deviation from mean and sd you can accept
deviation_mean <- 1.5
deviation_sd <- 1.5

# create empty container for resulting samples
samples <- list(n_replication)

# Repeatedly sample from length
i <- 0
sample_count <- 0

repeat {
  
  i <- i+1
  
  # take a sample from length
  sample_length <- sample(length, size_sample)
  
  # keep the sample when is is close enough
  if(abs(aimed_mean - mean(sample_length)) < deviation_mean &
  abs(aimed_sd - sd(sample_length)) < deviation_sd){
    
    samples[[i]] <- sample_length
    sample_count <- sample_count + 1
    
  }
  
  if(i == n_replication | sample_count == n_sample){
    break
  }
  
}

# your samples
samples

# test whether it worked
lapply(samples, function(x){abs(mean(x)-aimed_mean)<deviation_mean})
lapply(samples, function(x){abs(sd(x)-aimed_sd)<deviation_sd})