Descriptive statistics summarise the data you have. Inferential statistics use that data to make claims about a larger group you did not measure. Nearly every serious analytical mistake in business comes from doing the first and reporting it as though it were the second.
Descriptive statistics: what happened
Descriptive statistics are a summary. Counts, means, medians, percentages, standard deviations, charts - all of it describes the specific dataset in front of you and makes no claim beyond it.
"Our 412 orders last month averaged £38, with a median of £29." That is complete, true and requires no assumptions. If you have data on the whole population you care about - all your orders, all your staff - descriptive statistics may be all you need.
Inferential statistics: what it probably means
Inference goes further: from a sample to a population, or from the past to the future. It always comes with a stated level of uncertainty.
"Based on 412 sampled orders, we estimate the true average across all customers is between £35 and £41, with 95% confidence." Notice what has been added: a range, a confidence level, and an implicit claim that the sample represents the whole.
Confidence intervals, hypothesis tests, p-values, regression predictions - all inferential. All only valid if your sample was gathered properly.
The mistake that costs money
A business runs a two-week trial of a new landing page. Version B converts at 4.1%, version A at 3.6%. Someone writes "B is 14% better" and it gets rolled out.
That sentence is descriptive dressed as inferential. Descriptively, B did convert better in that fortnight. Inferentially - is B better in general? - the honest answer depends on sample size and variation, and with small traffic that gap is frequently pure noise. Half of all "wins" in poorly analysed tests reverse when repeated.
How to keep them straight
Ask one question: am I talking about the data I have, or about something beyond it?
- Past sales figures for reporting → descriptive
- Whether a change caused an improvement → inferential
- A customer survey used to describe respondents → descriptive
- A customer survey used to describe all customers → inferential (and now sampling matters enormously)
- Any forecast → inferential
Why the distinction matters for your credibility
Descriptive claims are hard to argue with. Inferential claims can be wrong, and stating them without their uncertainty is how analysts lose the trust of decision-makers. Adding "we are 95% confident the effect is between X and Y" is not hedging - it is the difference between analysis and assertion.
Learning to do both well
The Statistics for Business course covers descriptive summary, sampling and inference in sequence, so you know which claim you are making and what it rests on. Enquire about the next intake.