SAMPLING AND STANDARDIZATION 1

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A sample isdefined as a subset of people or events that are derived from alarger population that is analyzed and used to make a reference(Sukal, 2013). To have a sample that totally represents the entirepopulation, it should be selected randomly, and a larger area shouldbe taken into consideration. Population, on the other hand, refers toa set of entities that are under study (Kennedy, 1972). Whenconducting research, it is technically impossible to consult theentire population and as such, a sample is used.

The normaldistribution has various characteristics. To begin with, normaldistributions are symmetric around their mean whereas the area belowthe normal curve is usually equated to 1.0. On the other hand, themean, median and mode in a normal distribution are all equal. Otherfeatures of the normal distributions are that they are denser in thecenter and less dense in the tails (Sukal, 2013). Additionally, thetwo parameters used to define the normal distributions are the meanand standard deviation. The normal curves also exhibit certaincharacteristics, and they include skewness equated to zero as well asthe mean, median and mode being located at the center. Finally,dispersions can change in the normal curves.

The process ofstandardization is deemed as important for two primary reasons. Tobegin with, it attaches meaning to all scores while ensuring thatinterpretations can be made to all the existing data. Additionally,the concept allows for the comparison of two scores to beaccomplished directly (Sukal, 2013). The z-score provides an analysisof numbers whereby the original scores are quantified based on thenumber of standard deviations that the number is from the mean of thedistribution. A real life example where the z-scores are utilized isin a classroom situation whereby there is need to compare the testscores obtained by the students in a particular subject (Kennedy,1972).

Calculations

The formula for calculation of z-score is as follows:

z = x – μ / σ

11-18/5 = -1.4

The z-score indicates that the number of deviations was 1.4 belowthe mean of the raw scores.

17-18/5 = -0.2

The z-score indicates that the number of deviations was 0.2 belowthe mean of the raw scores.

21-18/5 = 0.6

The z-score indicates that the number of deviations was 0.6 abovethe mean of the raw scores.

25-18/5 = 1.4

The z-score indicates that the number of deviations was 1.4 abovethe mean of the raw scores.

References

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Kennedy, W. R. (1972). *Sampling, standards and homogeneity: Asymposium presented at the 75th annual meeting … Los Angeles,Calif., 25 – 30 June 1972*. Philadelphia, Pa: ASTM.

Sukal, M. (2013). Research methods: Applying statistics in research.San Diego, CA: Bridgepoint Education, Inc.

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