Arrange the following pairs of standard deviation (σ) and total number of samples (n) pertaining to different sampling distributions in the decreasing order of their standard error.

Standard error is the standard deviation divided by the square root of the sample size, giving values of 0.4, 0.3, 0.1 and 0.2.

Pair one gives 1.6 over four equals 0.4, the largest standard error.

Pair two gives 1.5 over five equals 0.3, the second largest.

Pair four gives 1.4 over seven equals 0.2, and pair three gives 0.6 over six equals 0.1, the smallest.

In decreasing order the sequence is therefore one, two, four, three.

Standard error shrinks as sample size grows, sharpening the estimate of the population mean.