Review question frameworks and applications

¶ … Statistical Research

In order to measure a given construct, the numerical data provided by the study's survey period is sorted to determine a baseline level. By determining the mean, median and mode from the various respondents, this baseline can be used to operationalize a particular construct. The Mean is defined as the mathematical average derived from a set of numerical figures, or the sum of every number in a given set divided by the number of figures comprising that sum. The concept of mean can be visualized as the "balance point" of any given distribution of numerical figures, and envisioning mean in this fashion is premised in basic physics, because if a basic data distribution were to appear fulcrum, the mean would be the point where perfect balance is achieved. Experienced statisticians incorporate mean within their analysis for several fundamental purposes, and "of all the measures of central tendency, the mean is viewed as the most reliable and stable & #8230; (and) can be very powerful with normal distributions where extreme scores cannot unduly influence it" (Keele, 2010). The Mode is merely the most frequently occurring numerical figure within a given distribution set, and "the mode is the only useful measure of central tendency when a variable is measured on a nominal scale. " (Keele, 2010). Because the mode represents the figure within a set that occurs with the most frequency, the mode is widely considered to be the probability center of a distribution, and if one were to randomly select a single figure from any distribution, the modal value is statistically expected to be observed at higher rate. The Median is defined as the numerical figure within a distribution that represents the middle of center, as determined when each of the values in set have been ordered in ascending order from least to most, and "for ordinal data, the median is the best indicator of central tendency" (Keele, 2010). One can also conceive of median as the specific point within a distribution which separates the number set into equal halves on both sides which, with 50% of the figures falling on either side of the median if the distribution were plotted on a number line, and for this reason the median is typically referred to as the visual center of a numerical distribution.