Final answer:
The key terms for a fitness center study are population (all clients), sample (subset of clients), parameter (average time for population), statistic (average time for sample), variable (exercise time per week), and data (observed exercise times). A personal trainer's expectations vs. actual weight lifting and variability in weight loss outcomes from a workout program are also discussed.
Step-by-step explanation:
In the context of a fitness center conducting a study to find out the average time a client exercises each week, the key terms can be defined as follows:
- The population is all the clients of the fitness center.
- The sample is a subset of the clients from which data will be collected.
- The parameter is the average time the entire population spends exercising in the center each week.
- The statistic is the average time the sample spends exercising, which is used to estimate the parameter.
- The variable is the amount of time a client exercises per week.
- The data are the actual measurements or observations of exercise time from the sample.
When a personal trainer evaluates clients' maximum weights lifted against expectations, the variables are the expected maximum weight and the actual maximum weight lifted, and the data is the recorded weights. Variability observed in outcomes, like weight loss in a group of people on a workout program, is attributable to biological differences and external factors influencing weight loss.