Grade9 sampling, data judgments and probability models
A sample is a method of selection, not just a smaller group
A survey asking only basketball players whether they play sports regularly over-represents people already involved in sport. A large number of answers does not automatically remove that selection bias. Define the population of interest, examine who could be included and identify whose views or outcomes are missing.
Question wording can also bias results. “Do you agree that the terrible new food should be changed?” supplies an evaluative judgment before asking for a response. A neutral question separates the respondent's assessment from the survey writer's preference. Order, mode and circumstances of collection can affect what the data support.
Interpret statistics within their scope
A mean uses every numerical value, while a median depends on ordered position. An extreme outlier can affect the mean strongly without changing the middle position in the same way. A summary can conceal different distributions, so inspect spread, clusters and unusual observations where available. A correlation or shared trend does not independently establish a causal mechanism.
In the supplied set 10,12,14,15,16, the mean is 67/5=13.4 and the median is 14. Adding 150 changes the mean to 217/6, approximately 36.17, while the new median is(14+15)/2=14.5. Those different effects explain why the choice of summary matters rather than prove one measure is always best.
Distinguish a model from an observation
Theoretical probability uses a defined sample space and assumptions about how outcomes occur. Experimental probability uses observed relative frequencies. A small trial sample can differ from a model without disproving it. Equally named outcomes do not necessarily have equal chances; check the physical or procedural conditions.
For combined events, specify whether selections are replaced and whether trials are independent. Drawing without replacement changes the remaining counts; a result from an independent fair trial does not make the next opposite result certain. A valid probability stays between zero and one, and complementary outcomes sum to one when they exhaust the possibilities.
Explain how the data or model connects to the conclusion. Neither a precise-looking graph nor a familiar formula justifies generalizing beyond the selected population or ignoring a stated condition.