Level 3 · A sample of 200 orders

Population and sample

The population is every item you care about: here, all 10,849 completed orders. A sample is the part you actually measure. When you have the whole population in a table, its mean is simply the answer. Samples exist because the population is often too big, too slow or too costly to measure: auditors checking invoices by hand, a survey of customers, an A/B test that can only run for two weeks.

sample = completed.sample(n=200, random_state=7)
sample["order_value"].mean()      # 515.22
completed["order_value"].mean()   # 543.30

random_state fixes the random draw so you (and the checker) get the same 200 rows every time.

Sampling error is normal

The sample mean is $28.08 below the population mean, and nothing is wrong with the sample. Each random sample gives a slightly different answer. Try other seeds:

random_state	sample mean
2	$384.70
5	$574.72
7	$515.22
8	$581.28

Same population, same size, a spread of almost $200. That spread is sampling error: the difference between a sample’s number and the population’s number that comes only from which rows happened to be drawn.

Why order values vary so much

A sample of 200 orders typically includes around six orders above $2,500. Draw two or three more or fewer of those and the mean moves by tens of dollars. The more skewed and spread out a column is, the more its sample means wander. The median of the same sample ($347.46 against $268.94 for all orders) shows that every statistic you compute from a sample has its own error.

Bigger samples wander less

Sampling error shrinks as the sample grows, but slowly: it falls with the square root of the sample size. Four times the sample halves the typical error. The boss level puts a number on this with the standard error.

Common mistakes

• Treating a sample’s number as the truth. Report it as an estimate, ideally with a margin.
• Reading sampling error as a finding. A sample that comes out lower than the books is not evidence of a problem until the gap is bigger than sampling error can explain.
• Rounding before subtracting. Round at the end; rounding each mean first can shift the difference by a cent.
• Sampling without a seed in an analysis others must reproduce. Without random_state, every run gives a different sample and a different answer.