Realities

Note:
  • Provide some context for your answers. For example, don’t just say “variability is everywhere.” Rather say something like “Variability is everywhere, specifically among individuals and among summaries computed from different samples.” Similarly, don’t just say “conclusions are uncertain.” Rather say “conclusions about the population from information in the sample are uncertain.”
  1. The three “realities” that, if they did not exist, would eliminate the need for the field of statistics are that (i) you cannot “see” the entire population and must, therefore, take a sample; (ii) variability is “everywhere,” both among individuals and among statistics; and (iii) conclusions about the population from information in the sample are uncertain.


Variability

Note:
  • In the second question.
    • Be specific to your example, don’t just say the “individuals differ” or the “samples differ.” For example, it is not adequate to say that each Bluegill will be different. Instead, be specific, and say (any one of these) each Bluegill will have a different length, different weight, or be of a different sex.
    • Your description of sampling variability should refer to a summary measure, usually the mean/average or percentage/proportion. For example, don’t say that two samples of Bluegills will differ. Rather, say (any one of these) two samples of Bluegill will have different mean lengths, mean weights, or percentage of females.
    • When describing sampling variability make sure that you describe repeated samples from the same population. For example, it would be incorrect to say that sampling variability is illustrated by the fact that Bluegill sampled from Lake A had a different mean length than Bluegill sampled from Lake B because Lake A and Lake B are not repeated samples from the same population; rather they are two different populations.
    • The answer below was just one example. Your situation will likely differ.
  1. Natural variability is the realization that no two individuals are exactly identical. Sampling variability is the realization that the results (statistics) from any two samples from the same population are not exactly identical.
  2. Consider a situation where a biologist is sampling Bluegill from a particular lake. Natural variability is the realization that no two Bluegill from this population will be exactly identical; i.e., their lengths, weights, number of scales, etc. will be different. Sampling variability is the realization that the results from any two samples of Bluegill from this population will not be identical. For example, the mean lengths from two samples of Bluegill from this population may differ, or the mean weights, or the mean number of scales, or the percentage of sexually mature fish.