STATISTIC VS PARAMETER 4
Accordingto Lyon (2014), we are surrounded by normal distributions. Fromheights of individualsto IQ test scores, to measurement errors, weights of objects,the age of people, to the number of ants in a colony,it is a contingent fact that all manner of things tendsto benormally distributed.
Thenormal distribution, also known as Gaussian distribution ischaracterizedby its symmetry around the mean. Anormal distribution is denser at the center and less densein the tails and the total area under the curve is 1 (Simon,2015).
Aparameteris a summary number, such as a percentage or an average which is usedto describe an entire population. In the real world,however, obtaining the values of parameters is sometimes costly,unpractical and at times impossible hence the need for sampling.
Ifa sample is completely random and large enough to represent the wholepopulation, then the informationcollected from the sample can be used tomake inferences about the particular population. A statistic, whichis a measurable characteristic of a sample, is used to makeinferences abouta population parameter.Thisis possible because it has beenproventhat the sample statistics are unbiasedestimators of the population parameters("Populations, Samples, Parameters, and Statistics,"2016)
Inthe given case scenario, the population meanis given as seventy-five (75), and therefore, the value of the samplemean that best estimates it should be exactly 75 or a value closer toit. Graph A, C, and D each has a mean value near the actualpopulation mean of 75,and at firstglanceappearunbiased estimators. However, upon further inspection, A is the graphwhich actually would be used to best represent the estimator for thepopulation statistic. Thisis because the graph is symmetric around the mean and if a smoothcurve weredrawnover its peaks, it would have a bell shape which is the shape thatcharacterizes all normal distributions. The graph of A is consideredto be a normal distribution despite having a larger spread towardsthe right.
Thegraph of statistic B has a bell shape and can beregardedas anormalcurve,but it is not symmetrical around the mean. Because of this, thisgraph does not give an accurate estimate of the population mean.Perhaps if the graphhad been symmetric about the given mean, it would have beenconsidered a better estimator than all the other statistics A, C,and D.
Thegraph of statistic D follows a uniform distribution. However, in reallife, the views of people do not often follow a uniform distribution,and hence the graphis not a good estimator of the population mean despite it having ameancloser to the actual populations mean. Whenthe graphs of C and D are compared, both have a mean closer to theactual papameter but the graph of statistic C has a smallervariability indicating that it would produce better populationestimates to the actual population parameter when compared with thegraph of statistic D.
Eventhough the graphs of the sample distributions A, B, C, and D can beused as estimators of different population parameters, distributionA, in this case, will be the best choice to describe the populationparameter.
Lyon,A. (2014). Why are Normal Distributions Normal? BritishJournal for The Philosophy of Science,63(5).Retrieved fromhttp://aidanlyon.com/aidanlyon.com/media/publications/Lyon-normal_distributions.pdf
Populations,Samples, Parameters, and Statistics.(2016). Cliffsnotes.com.Retrieved 20 March 2017, fromhttps://www.cliffsnotes.com/study-guides/statistics/sampling/populationssamples-parameters-and-statistics
Simon,J. (2015). What Does the Normal Curve Mean? TheJournal Of Educational Research,61(10),435-438. Retrieved fromhttp://www.tandfonline.com/doi/abs/10.1080/00220671.1967.10883726