Core distinction and conditions
A statistical description is useful only when its meaning matches the question. A linear correlation coefficient describes direction through its sign and strength through its absolute magnitude. Negative is not the same as absent. The arithmetic mean uses every value in a sum divided by the number of observations. The median uses the middle of the ordered data, with the central pair averaged when the count is even. These descriptions answer different questions and can react differently to an extreme observation. Neither a coefficient nor a center measure by itself explains why the observations occurred.
Worked example: follow the calculation
Suppose a fictional class records five practice durations: 1, 3, 4, 7 and 20 minutes. The sum is 35, so the mean is seven minutes; the ordered middle value is four. If the last value is corrected to 30, the sum becomes 45 and the mean nine, while the median remains four. The result follows from this list: the endpoint changed the sum but did not change the third ordered observation. Do not turn the example into a claim that a median is immune to every kind of data change. Changing central values or the observation count can change it.
Compare what a result does and does not say
A coefficient of -0.6 describes a stronger linear relationship than +0.2, while pointing in the opposite direction. It does not establish a cause, even if the association seems sensible. Statistical significance is also distinct from the magnitude or practical meaning of an effect. To judge practical importance, ask for an effect-size estimate, the measurement unit and the context of the difference. A large sample can support a significance decision about a small difference. No significance label guarantees a useful change for every individual or replaces examination of design, measurement and generalizability.
Transfer check: match question to evidence
A report gives a negative correlation and calls a group difference significant. Can you infer that the association is weak or that the difference is practically large? Neither conclusion follows: use the absolute coefficient for linear strength and request magnitude information for the group difference. As a calculation check, replace one large endpoint in an ordered five-value list and explain separately what happens to the sum and middle value. You have completed the task when each conclusion can be traced to the statistic or calculation that supports it, with causal and individual predictions left outside what the data establish.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which evidence or rule supports your decision and why the alternatives do not fit.
Sources & authorship
Original OpenExam explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
OpenStax Psychology 2e, section 2-3OpenStax Introductory Statistics 2e, section 2.5College Board AP Psychology ced